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A175070
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a(n) is the sum of perfect divisors of n - n, where a perfect divisor of n is a divisor d such that d^k = n for some k >= 1.
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3
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0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 3, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10
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OFFSET
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1,4
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COMMENTS
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a(1) = 0, for n >=2: a(n) = sum of perfect divisors of n less than n.
a(n) > 0 for perfect powers n = A001597(m) for m > 2.
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LINKS
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FORMULA
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PROG
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(PARI) A175070(n) = if(!ispower(n), 0, sumdiv(n, d, if((d>1)&&(d<n)&&((d^valuation(n, d))==n), d, 0))); \\ Antti Karttunen, Jun 12 2018
(PARI) first(n) = {my(res = vector(n)); for(i = 2, sqrtint(n), for(j = 2, logint(n, i), res[i^j] += i)); res} \\ David A. Corneth, Jun 12 2018
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CROSSREFS
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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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