A069519 Numbers k such that 1/(Sum_{d|k} (-1)^d/d) is an integer.

1, 2, 4, 8, 12, 16, 24, 32, 48, 56, 64, 96, 112, 120, 128, 192, 224, 240, 256, 384, 448, 480, 512, 528, 672, 768, 896, 960, 992, 1024, 1056, 1344, 1456, 1536, 1792, 1920, 1984, 2048, 2112, 2160, 2208, 2688, 2912, 3072, 3584, 3840, 3968, 4096, 4224, 4320

Offset: 1

Author

Benoit Cloitre, Apr 16 2002

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..4907 (terms below 10^11)

Crossrefs

Cf. A066192.

Programs

Mathematica

q[n_] := IntegerQ[1/DivisorSum[n, (-1)^# / # &]]; Select[Range[4500], q] (* Amiram Eldar, Apr 27 2025 *)

PARI

isok(k) = denominator(1/sumdiv(k, d, (-1)^d/d)) == 1; \\ Amiram Eldar, Apr 27 2025

Formula

a(1)=1, a(2)=2, a(n) = A066192(n-2) for n > 2.

Extensions

Name corrected by Amiram Eldar, Apr 27 2025