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A359546
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a(n) = 1 if there is no factor of the form p^p in n, but for some k-th arithmetic derivative (k >= 1) of n such a factor exists; otherwise 0.
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7
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1
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OFFSET
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1
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COMMENTS
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Question: What can be said about the distribution of 0's and 1's in this sequence? Compare also to A328308, A341996 and A359543.
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LINKS
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FORMULA
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a(n) = [A256750(n) < 0], where [ ] is the Iverson bracket.
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EXAMPLE
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a(15) = 1, because although 15 itself is not in A100716, its arithmetic derivative 15' = 8 is there.
a(26) = 1, as although neither 26 nor 26' = 15 are in A100716, the second derivative of 26, 26'' = 15' = 8 is there.
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PROG
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(PARI)
A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = (f[k, 2]>=f[k, 1])); factorback(f); };
A341999(n) = if(!n, n, while(n>1, n = A003415checked(n)); (!n));
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CROSSREFS
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Characteristic function of A359547.
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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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