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

1,1

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

Prog

(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);

Crossrefs

Cf. A003415, A100716, A129251, A327965.

Indices of nonzero terms in A327928.

Cf. A099309, A327934 for subsequences.

Sequence in context: A190679 A009023 A099309 * A327864 A235865 A311086

Adjacent sequences: A327926 A327927 A327928 * A327930 A327931 A327932

Keyword

nonn

Author

Antti Karttunen, Oct 01 2019

Status

approved