A346473 a(n) = A250469(n) - sigma(n).

0, 0, 1, 2, 1, 3, 3, 6, 12, 9, 1, 5, 3, 15, 11, 14, 1, 12, 3, 15, 23, 27, 5, 9, 18, 33, 25, 25, 1, 15, 5, 30, 37, 45, 29, 14, 3, 51, 39, 27, 1, 27, 3, 45, 37, 63, 5, 17, 64, 54, 53, 55, 5, 39, 19, 45, 65, 81, 1, 9, 5, 87, 51, 62, 35, 51, 3, 75, 79, 63, 1, 18, 5, 105, 61, 85, 47, 63, 3, 51, 84, 117, 5, 25, 25, 123, 95

Offset: 1

Author

Antti Karttunen, Jul 28 2021

Keywords

• sign
• look

Comments

The first negative term is a(120) = -3.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences generated by sieves
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A001359, A250469, A280692, A286385.

Programs

Mathematica

Block[{g}, g[n_] := If[n == 1, 0, PrimePi@FactorInteger[n][[1, 1]]]; Function[s, MapIndexed[Lookup[s, g[First@ #2] + 1][[#1]] - Boole[First@ #2 == 1] - DivisorSigma[1, First@ #2] &, #] &@ Map[Position[Lookup[s, g@ #], #][[1, 1]] &, Range@ 120]]@ PositionIndex@ Array[g, 10^4]] (* Michael De Vlieger, Oct 18 2021 *)

PARI

A346473(n) = A250469(n)-sigma(n);

Formula

a(n) = A250469(n) - A000203(n).

a(n) = A286385(n) - A280692(n).

a(A001359(n)) = 1 for all n >= 1.