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A327929
Numbers for which there is at least one such prime p that p^p divides the arithmetic derivative of n, A003415(n).
18
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
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
Indices of nonzero terms in A327928.
Cf. A099309, A327934 for subsequences.
Sequence in context: A190679 A009023 A099309 * A327864 A235865 A311086
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 01 2019
STATUS
approved