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A341996 a(n) = 1 if there is at least one such prime p that p^p divides the arithmetic derivative of n, A003415(n); a(0) = a(1) = 0 by convention. 5
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, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for characteristic functions

FORMULA

a(n) = [A327928(n)>0], where [ ] is the Iverson bracket.

For all n > 1, a(n) >= [A129251(n)>0], i.e., if A129251(n) is nonzero, then certainly a(n) = 1.

For all n >= 0, a(n) <= A341999(n).

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)));

A341996(n) = (A327928(n)>0);

CROSSREFS

Characteristic function of A327929.

Cf. A003415, A129251, A327928, A341994, A341995, A341997, A341999.

Differs from A327928 for the first time at n=81, where a(81)=1.

Sequence in context: A188009 A144596 A188187 * A341999 A118685 A244063

Adjacent sequences:  A341993 A341994 A341995 * A341997 A341998 A341999

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 28 2021

STATUS

approved

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Last modified June 14 05:51 EDT 2021. Contains 345018 sequences. (Running on oeis4.)