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A326136 a(n) = sigma(n) - sigma(A028234(n)), where sigma is the sum of divisors of n, and A028234 gives n without any occurrence of its smallest prime factor.

%I A326136 #9 Dec 21 2024 11:09:59
%S A326136 0,2,3,6,5,8,7,14,12,12,11,24,13,16,18,30,17,26,19,36,24,24,23,56,30,
%T A326136 28,39,48,29,48,31,62,36,36,40,78,37,40,42,84,41,64,43,72,72,48,47,
%U A326136 120,56,62,54,84,53,80,60,112,60,60,59,144,61,64,96,126,70,96,67,108,72,96,71,182,73,76,93,120,84,112,79,180,120,84,83
%N A326136 a(n) = sigma(n) - sigma(A028234(n)), where sigma is the sum of divisors of n, and A028234 gives n without any occurrence of its smallest prime factor.
%H A326136 Antti Karttunen, <a href="/A326136/b326136.txt">Table of n, a(n) for n = 1..20000</a>
%H A326136 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A326136 a(n) = A000203(n) - A000203(A028234(n)).
%F A326136 From _Amiram Eldar_, Dec 21 2024: (Start)
%F A326136 a(n) = A000203(n) - A326135(n).
%F A326136 Sum_{k=1..n} a(k) ~ (zeta(2)/2) * (1 - c) * n^2, where c is defined in the corresponding formula in A326135. (End)
%o A326136 (PARI)
%o A326136 A028234(n) = { my(f = factor(n)); if (#f~, f[1, 1] = 1); factorback(f); }; \\ From A028234
%o A326136 A326136(n) = (sigma(n) - sigma(A028234(n)));
%Y A326136 Cf. A000203, A013661, A028234, A326066, A326135.
%K A326136 nonn
%O A326136 1,2
%A A326136 _Antti Karttunen_, Jun 08 2019