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A112621
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If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = sum_{p|n} b(p,n)^b(p,n).
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2
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0, 1, 1, 4, 1, 2, 1, 27, 4, 2, 1, 5, 1, 2, 2, 256, 1, 5, 1, 5, 2, 2, 1, 28, 4, 2, 27, 5, 1, 3, 1, 3125, 2, 2, 2, 8, 1, 2, 2, 28, 1, 3, 1, 5, 5, 2, 1, 257, 4, 5, 2, 5, 1, 28, 2, 28, 2, 2, 1, 6, 1, 2, 5, 46656, 2, 3, 1, 5, 2, 3, 1, 31, 1, 2, 5, 5, 2, 3, 1, 257, 256, 2, 1, 6, 2, 2, 2, 28, 1, 6, 2, 5, 2, 2, 2, 3126, 1, 5, 5, 8, 1, 3, 1, 28, 3
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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45 = 3^2 * 5^1. So a(45) = 2^2 + 1^1 = 5.
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MATHEMATICA
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f[n_] := Block[{fi = Last@Transpose@FactorInteger@n}, Plus @@ (fi^fi)]; Rest@Array[f, 92] (* Robert G. Wilson v *)
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PROG
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(PARI) A112621(n) = { my(f = factor(n), s = 0); for (k=1, #f~, s += (f[k, 2]^f[k, 2]); ); s; } \\ Antti Karttunen, May 28 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Term a(1) = 0 prepended, data section extended to 105 terms - Antti Karttunen, May 28 2017
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STATUS
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approved
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