{"paper":{"title":"On the Reciprocal of the Binary Generating Function for the Sum of Divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexander Riasanovsky, Joshua Cooper","submitted_at":"2014-09-09T22:30:39Z","abstract_excerpt":"If \\(A \\) is a set of natural numbers containing \\(0 \\), then there is a unique nonempty \"reciprocal\" set \\(B \\) of natural numbers (containing \\(0 \\)) such that every positive integer can be written in the form \\(a + b \\), where \\(a \\in A \\) and \\(b \\in B \\), in an even number of ways. Furthermore, the generating functions for \\(A \\) and \\(B \\) over \\(\\FF_2 \\) are reciprocals in \\(\\FF_2 [[q]] \\). We consider the reciprocal set \\(B \\) for the set \\(A \\) containing \\(0 \\) and all integers such that \\(\\sigma(n) \\) is odd, where \\(\\sigma(n) \\) is the sum of all the positive divisors of \\(n \\). Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2909","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}