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A349322
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a(n) = Sum_{d|n} d^c(d), where c is the characteristic function of refactorable numbers (A336040).
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5
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1, 3, 2, 4, 2, 5, 2, 12, 11, 5, 2, 18, 2, 5, 4, 13, 2, 32, 2, 7, 4, 5, 2, 50, 3, 5, 12, 7, 2, 9, 2, 14, 4, 5, 4, 81, 2, 5, 4, 55, 2, 9, 2, 7, 14, 5, 2, 52, 3, 7, 4, 7, 2, 34, 4, 71, 4, 5, 2, 83, 2, 5, 14, 15, 4, 9, 2, 7, 4, 9, 2, 185, 2, 5, 6, 7, 4, 9, 2, 136, 13, 5, 2, 107
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OFFSET
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1,2
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COMMENTS
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For each divisor d of n, add d if d is refactorable (i.e., if the number of divisors of d divides d), otherwise add 1. For example, the divisors of 8 are 1,2,4,8 and the refactorable divisors of 8 are 1,2,8. The sum is then a(8) = 1 + 2 + 1 + 8 = 12.
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LINKS
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FORMULA
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MATHEMATICA
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a[n_] := DivisorSum[n, If[Divisible[#, DivisorSigma[0, #]], #, 1] &]; Array[a, 100] (* Amiram Eldar, Nov 16 2021 *)
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PROG
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(PARI) isrf(n) = n%numdiv(n)==0; \\ A336040
a(n) = sumdiv(n, d, if (isrf(d), d, 1)); \\ Michel Marcus, Nov 16 2021
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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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