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A327928
Number of distinct primes p such that p^p divides the arithmetic derivative of n.
12
0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0
OFFSET
0,82
LINKS
FORMULA
a(0) = a(1) = 0; for n > 1, a(n) = A129251(A003415(n)).
EXAMPLE
For n=20, A003415(20) = 24 = 2^3 * 3^1, thus only 2^2 divides 24, and a(24) = 1.
For n=81, A003415(81) = 108 = 2^2 * 3^3. Both 2^2 and 3^3 divide 108, thus a(81) = 2.
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)));
CROSSREFS
Cf. A003415, A129251, A327929 (indices of nonzero terms), A327932.
Sequence in context: A236233 A112607 A161371 * A364387 A147645 A091970
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 01 2019
STATUS
approved