A327929 Numbers for which there is at least one such prime p that p^p divides the arithmetic derivative of n, A003415(n).

4, 8, 12, 15, 16, 20, 24, 27, 28, 32, 35, 36, 39, 40, 44, 48, 51, 52, 54, 55, 56, 60, 64, 68, 72, 76, 80, 81, 84, 87, 88, 91, 92, 95, 96, 100, 104, 108, 111, 112, 115, 116, 119, 120, 123, 124, 128, 132, 135, 136, 140, 143, 144, 148, 152, 155, 156, 158, 159, 160, 162, 164, 168, 172, 176, 180, 183, 184, 187, 188, 189, 192, 196, 200

Offset: 1

Author

Antti Karttunen, Oct 01 2019

Keywords

• nonn

Comments

Numbers k such that A327928(k) = A129251(A003415(k)) is > 0, i.e., numbers whose arithmetic derivative is in A100716.

For all n, A003415(a(n)) is also present in this sequence and A003415(a(n)) = m * A327965(a(n)) for some m > 1.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..30000

Crossrefs

Cf. A003415, A100716, A129251, A327965.

Indices of nonzero terms in A327928.

Cf. A099309, A327934 for subsequences.

Programs

PARI

A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A129251(n) = { my(f = factor(n)); sum(k=1, #f~, (f[k, 2]>=f[k, 1])); };
A327928(n) = if(n<=1,0,A129251(A003415(n)));
isA327929(n) = (A327928(n)>0);