cp's OEIS Frontend

A378663 Number of divisors d of n such that sigma(d) < 2*d < A003961(d), where A003961 is fully multiplicative with a(p) = nextprime(p).

%I A378663 #9 Dec 06 2024 10:25:39
%S A378663 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 A378663 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 A378663 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 A378663 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 A378663 Number of terms of A341615 that divide n.
%H A378663 Antti Karttunen, <a href="/A378663/b378663.txt">Table of n, a(n) for n = 1..100000</a>
%H A378663 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>
%H A378663 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A378663 a(n) = Sum_{d|n} A341613(d).
%F A378663 a(n) = A337345(n) - A341620(n).
%F A378663 a(n) = A378662(n) - A080225(n).
%o A378663 (PARI)
%o A378663 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A378663 A341613(n) = ((sigma(n)<(2*n))&&((2*n)<A003961(n)));
%o A378663 A378663(n) = sumdiv(n,d,A341613(d));
%Y A378663 Inverse Möbius transform of A341613.
%Y A378663 Cf. A000203, A003961, A080225, A337345, A341615, A341620, A378662.
%K A378663 nonn
%O A378663 1,8
%A A378663 _Antti Karttunen_, Dec 06 2024