cp's OEIS Frontend

A337541 Number of divisors d of n for which sigma(A003961(d)) >= 2*sigma(d), where sigma is the sum of divisors, and A003961(x) shifts the prime factorization of x one step towards larger primes.

%I A337541 #9 Aug 31 2020 10:23:17
%S A337541 0,0,0,0,0,1,0,1,1,0,0,2,0,1,1,2,0,3,0,1,1,0,0,4,0,0,2,2,0,3,0,3,0,0,
%T A337541 1,5,0,0,0,3,0,4,0,1,3,0,0,6,1,1,0,1,0,5,0,4,0,0,0,6,0,0,3,4,0,2,0,1,
%U A337541 0,3,0,8,0,0,2,1,0,2,0,5,3,0,0,7,0,0,0,3,0,7,0,1,0,0,0,8,0,3,2,3,0,2,0,3,4
%N A337541 Number of divisors d of n for which sigma(A003961(d)) >= 2*sigma(d), where sigma is the sum of divisors, and A003961(x) shifts the prime factorization of x one step towards larger primes.
%C A337541 Number of terms of A337381 that divide n.
%H A337541 Antti Karttunen, <a href="/A337541/b337541.txt">Table of n, a(n) for n = 1..65537</a>
%H A337541 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A337541 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A337541 a(n) = Sum_{d|n} A337383(d).
%F A337541 a(n) = A337542(n) + A337383(n).
%o A337541 (PARI)
%o A337541 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A337541 A337541(n) = sumdiv(n,d,sigma(A003961(d))>=2*sigma(d));
%Y A337541 Inverse Möbius transform of A337383.
%Y A337541 Cf. A000203, A003961, A003973, A337381, A337542, A337543 (positions of ones).
%Y A337541 Cf. also A337345.
%K A337541 nonn
%O A337541 1,12
%A A337541 _Antti Karttunen_, Aug 31 2020