cp's OEIS Frontend

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.

%I A184396 #11 Aug 24 2017 16:37:26
%S A184396 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,
%T A184396 38,36,50,28,64,30,57,44,50,44,82,36,56,52,82,40,88,42,78,72,68,46,
%U A184396 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
%N 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.
%C A184396 Sequence is not the same as A065608(n): a(66) = 137, A065608(66) = 136.
%H A184396 Antti Karttunen, <a href="/A184396/b184396.txt">Table of n, a(n) for n = 1..10000</a>
%F A184396 a(n) = A000203(n) - A184395(n).
%e A184396 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.
%t A184396 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]
%o A184396 (PARI)
%o A184396 A184395(n) = length(vecsort(apply(d->sigma(d),divisors(n)), , 8));
%o A184396 A184396(n) = (sigma(n) - A184395(n)); \\ _Antti Karttunen_, Aug 24 2017
%Y A184396 Cf. A000203, A065608, A184395.
%K A184396 nonn
%O A184396 1,3
%A A184396 _Jaroslav Krizek_, Jan 12 2011
%E A184396 More terms from _Antti Karttunen_, Aug 24 2017