A378663 - OEIS

%I #9 Dec 06 2024 10:25:39

%S 0,0,0,1,0,0,0,2,1,1,0,1,0,1,1,3,0,1,0,2,1,0,0,2,0,0,2,2,0,2,0,4,0,0,

%T 1,2,0,0,1,3,0,2,0,2,3,0,0,3,1,2,0,2,0,2,0,3,1,0,0,3,0,0,3,5,0,0,0,2,

%U 1,3,0,3,0,0,2,2,0,1,0,4,3,0,0,3,0,0,0,3,0,4,1,2,0,0,0,4,0,3,2,3,0,0,0,3,4

%N Number of divisors d of n such that sigma(d) < 2*d < A003961(d), where A003961 is fully multiplicative with a(p) = nextprime(p).

%C Number of terms of A341615 that divide n.

%H Antti Karttunen, <a href="/A378663/b378663.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>

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

%F a(n) = Sum_{d|n} A341613(d).

%F a(n) = A337345(n) - A341620(n).

%F a(n) = A378662(n) - A080225(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 A341613(n) = ((sigma(n)<(2*n))&&((2*n)<A003961(n)));

%o A378663(n) = sumdiv(n,d,A341613(d));

%Y Inverse Möbius transform of A341613.

%Y Cf. A000203, A003961, A080225, A337345, A341615, A341620, A378662.

%K nonn,new

%O 1,8

%A _Antti Karttunen_, Dec 06 2024