cp's OEIS Frontend

A337345 Number of divisors d of n for which A003961(d) > 2*d, where A003961 is fully multiplicative with a(p) = nextprime(p).

%I A337345 #14 Dec 10 2024 17:25:46
%S A337345 0,0,0,1,0,1,0,2,1,1,0,3,0,1,1,3,0,3,0,3,1,0,0,5,0,0,2,3,0,4,0,4,0,0,
%T A337345 1,6,0,0,1,5,0,4,0,2,3,0,0,7,1,2,0,2,0,5,0,5,1,0,0,8,0,0,3,5,0,2,0,2,
%U A337345 1,4,0,9,0,0,2,2,0,3,0,7,3,0,0,8,0,0,0,4,0,8,1,2,0,0,0,9,0,3,2,5,0,2,0,4,4
%N A337345 Number of divisors d of n for which A003961(d) > 2*d, where A003961 is fully multiplicative with a(p) = nextprime(p).
%C A337345 Number of terms of A246282 that divide n.
%C A337345 Number of divisors d of n for which A048673(d) > d.
%H A337345 Antti Karttunen, <a href="/A337345/b337345.txt">Table of n, a(n) for n = 1..65537</a>
%H A337345 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A337345 a(n) = Sum_{d|n} A252742(d).
%F A337345 a(n) = A337346(n) + A252742(n).
%F A337345 From _Antti Karttunen_, Dec 10 2024: (Start)
%F A337345 a(n) = 1 <=> A341609(n) = 1.
%F A337345 a(n) = A378662(n) + A080224(n) = A378663(n) + A341620(n).
%F A337345 (End)
%o A337345 (PARI)
%o A337345 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A337345 A337345(n) = sumdiv(n,d,A003961(d)>(d+d));
%Y A337345 Inverse Möbius transform of A252742.
%Y A337345 Cf. A003961, A048673, A246282, A337346, A337372 (positions of ones), A341609 (their characteristic function), A341610 (positions of terms > 1), A378658 [= a(A091191(n))], A378662, A378663.
%Y A337345 Cf. also A080224, A337541, A341620.
%K A337345 nonn
%O A337345 1,8
%A A337345 _Antti Karttunen_, Aug 27 2020