A327929 - OEIS

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

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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])); };