cp's OEIS Frontend

A326135 a(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 A326135 #16 Mar 19 2025 05:54:51
%S A326135 1,1,1,1,1,4,1,1,1,6,1,4,1,8,6,1,1,13,1,6,8,12,1,4,1,14,1,8,1,24,1,1,
%T A326135 12,18,8,13,1,20,14,6,1,32,1,12,6,24,1,4,1,31,18,14,1,40,12,8,20,30,1,
%U A326135 24,1,32,8,1,14,48,1,18,24,48,1,13,1,38,31,20,12,56,1,6,1,42,1,32,18,44,30,12,1,78,14,24,32,48,20,4,1
%N A326135 a(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 A326135 Antti Karttunen, <a href="/A326135/b326135.txt">Table of n, a(n) for n = 1..16384</a>
%H A326135 Antti Karttunen, <a href="/A326135/a326135.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A326135 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A326135 a(n) = A000203(A028234(n)).
%F A326135 a(n) = A326065(n) / A000203(A020639(n)^(A067029(n)-1)).
%F A326135 Sum_{k=1..n} a(k) ~ (zeta(2)/2) * c * n^2, where c = Sum_{p prime} ((1/(p^2-1)) * Product_{prime q <= p} ((q-1)^2*(q+1)/q^3)) = 0.166218264542... . - _Amiram Eldar_, Dec 21 2024
%o A326135 (PARI)
%o A326135 A028234(n) = { my(f = factor(n)); if (#f~, f[1, 1] = 1); factorback(f); }; \\ From A028234
%o A326135 A326135(n) = sigma(A028234(n));
%Y A326135 Cf. A000203, A013661, A028234, A326065, A326136.
%K A326135 nonn
%O A326135 1,6
%A A326135 _Antti Karttunen_, Jun 08 2019