A184396 a(n) = number of numbers k <= sigma(n) such that k is not equal to sigma(d) for any divisor d of n, where sigma = A000203.

0, 1, 2, 4, 4, 8, 6, 11, 10, 14, 10, 22, 12, 20, 20, 26, 16, 33, 18, 36, 28, 32, 22, 52, 28, 38, 36, 50, 28, 64, 30, 57, 44, 50, 44, 82, 36, 56, 52, 82, 40, 88, 42, 78, 72, 68, 46, 114, 54, 87, 68, 92, 52, 112, 68, 112, 76, 86, 58, 156, 60, 92, 98, 120, 80, 137, 66, 120, 92, 136, 70, 183, 72, 110, 118, 134, 92, 160, 78, 176, 116

Offset: 1

Author

Jaroslav Krizek, Jan 12 2011

Keywords

• nonn

Comments

Sequence is not the same as A065608(n): a(66) = 137, A065608(66) = 136.

Examples

			For n = 4, sigma(4) = 7, from numbers 1 - 7 there are four numbers k such that k is not equal to sigma(d) for any divisor d of n: 2, 4, 5, 6; a(4) = 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A065608, A184395.

Programs

Mathematica

f[n_] := Block[{c = 0, k = 1, lmt = DivisorSigma[1, n] + 1, sd = DivisorSigma[1, #] & /@ Divisors@ n}, While[k < lmt, If[! MemberQ[sd, k], c++]; k++]; c]; Array[f, 67]

PARI

A184395(n) = length(vecsort(apply(d->sigma(d),divisors(n)), , 8));
A184396(n) = (sigma(n) - A184395(n)); \\ Antti Karttunen, Aug 24 2017

Formula

a(n) = A000203(n) - A184395(n).

Extensions

More terms from Antti Karttunen, Aug 24 2017