A387707 a(n) = A337345(A023196(n)), where A337345 is the number of divisors d of n for which A003961(d) > 2*d, and A023196 lists the nondeficient numbers, numbers k such that sigma(k) >= 2*k.

1, 3, 3, 3, 5, 3, 4, 6, 5, 4, 7, 5, 5, 8, 2, 4, 9, 3, 7, 8, 4, 8, 9, 5, 2, 4, 9, 7, 3, 12, 8, 6, 3, 8, 12, 7, 7, 9, 7, 12, 2, 6, 14, 2, 11, 6, 6, 8, 6, 6, 11, 13, 6, 2, 9, 7, 7, 16, 2, 14, 2, 6, 10, 12, 6, 7, 12, 2, 15, 8, 13, 6, 6, 6, 11, 2, 11, 12, 8, 16, 6, 7, 6, 7, 8, 2, 20, 7, 2, 6, 6, 12, 6, 13, 9, 9, 12, 11, 2

Offset

1,2

Comments

For all n > 1, a(n) > 1. See A337372 for a proof.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to prime indices in the factorization of n.

Index entries for sequences related to sigma(n).

Formula

For all n, a(n) >= A387708(n). [Because A337381 is a subsequence of A246282].

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A337345(n) = sumdiv(n, d, A003961(d)>(2*d));
k=0; n=0; while(k<105, n++; if(sigma(n)>=2*n, k++; print1(A337345(n), ", ")));

Crossrefs

Cf. A000203, A003961, A023196, A246282, A337345, A337372, A378658 (subsequence).

Cf. also A337381, A387708.

Sequence in context: A344186 A132448 A132450 * A132424 A070864 A321790

Adjacent sequences: A387704 A387705 A387706 * A387708 A387709 A387710

Keyword

nonn

Author

Antti Karttunen, Sep 08 2025

Status

approved