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A341996
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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.
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13
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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
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OFFSET
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0
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COMMENTS
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LINKS
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FORMULA
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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).
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PROG
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(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])); };
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CROSSREFS
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Characteristic function of A327929.
Positions of zeros is given by {0, 1} U A358215.
Differs from A327928 for the first time at n=81, where a(81)=1.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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