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Define \\begin{equation*}\n  \\mathcal{S}_{k}(x)=\\sum_{\\substack{1\\leqslant n_1,n_2,n_3 \\leqslant x^{1/2} \\\\ 1\\leqslant n_4\\leqslant x^{1/k} }} d(n_1^2+n_2^2+n_3^2+n_4^k),\n  \\qquad 3\\leqslant k\\in \\mathbb{N}. \\end{equation*} In this paper, we establish an asymptotic formula of $\\mathcal{S}_k(x)$ and prove that \\begin{equation*}\n  \\mathcal{S}_k(x)=C_1(k)x^{3/2+1/k}\\log x+C_2(k)x^{3/2+1/k}+O(x^{3/2+1/k-\\delta_k+\\varepsilon}), \\end{equation*} where $C_1(k),\\,C_2(k)$ are two constants depending only on $k,$ with $\\delta_3=\\frac{19}{60},\\,\\delta_4=\\fra","authors_text":"Jinjiang Li, Min Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-24T12:50:48Z","title":"On the Sum of Divisors of Mixed Powers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07610","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1d470775a0d29a97d5970d29fe318b177e40aab2566767e959431a137c123dff","target":"record","created_at":"2026-05-18T01:03:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6f204306c9f2de510e4a6434083f44c94ca957d425d690c31240c0da56b71f1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-24T12:50:48Z","title_canon_sha256":"eca877c8c26412ce87c2162779b7ee008a0e3f23fa02b38125fbc0bd5f3ebf99"},"schema_version":"1.0","source":{"id":"1609.07610","kind":"arxiv","version":1}},"canonical_sha256":"5c2251bae4ae7df160e1fe8ad32f85c39e27e8ea8f847846716740ef3e5efbef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c2251bae4ae7df160e1fe8ad32f85c39e27e8ea8f847846716740ef3e5efbef","first_computed_at":"2026-05-18T01:03:55.915683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:55.915683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iPXMYWFXRq/HFf/vG7KacNDiN6TEuUHnJQRDiZRMfOZ6EuXQ434SGenGW6IQBf2c8sjAKVImoX70GaF0pJbGDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:55.916337Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07610","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d470775a0d29a97d5970d29fe318b177e40aab2566767e959431a137c123dff","sha256:963e5b39f11cf68064277d2657b0d7659fd30b026d89dbae7022c9a07fde4fef"],"state_sha256":"066ef796a189623db8006cf39eca0dc7a2fe6a2657e294cdda96245fa8662e45"}