login
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.
5

%I #9 Aug 31 2020 10:23:17

%S 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 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 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 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 Number of terms of A337381 that divide n.

%H Antti Karttunen, <a href="/A337541/b337541.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = Sum_{d|n} A337383(d).

%F a(n) = A337542(n) + A337383(n).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A337541(n) = sumdiv(n,d,sigma(A003961(d))>=2*sigma(d));

%Y Inverse Möbius transform of A337383.

%Y Cf. A000203, A003961, A003973, A337381, A337542, A337543 (positions of ones).

%Y Cf. also A337345.

%K nonn

%O 1,12

%A _Antti Karttunen_, Aug 31 2020