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A343300
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a(n) is p1^1 + p2^2 + ... + pk^k where {p1,p2,...,pk} are the distinct prime factors in ascending order in the prime factorization of n.
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3
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0, 2, 3, 2, 5, 11, 7, 2, 3, 27, 11, 11, 13, 51, 28, 2, 17, 11, 19, 27, 52, 123, 23, 11, 5, 171, 3, 51, 29, 136, 31, 2, 124, 291, 54, 11, 37, 363, 172, 27, 41, 354, 43, 123, 28, 531, 47, 11, 7, 27, 292, 171, 53, 11, 126, 51, 364, 843, 59, 136, 61, 963, 52, 2, 174, 1342, 67, 291, 532, 370, 71, 11, 73
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OFFSET
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1,2
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COMMENTS
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a(n) depends only on prime factors of n (see formulas).
Primes are fixed points of this sequence.
Terms are in increasing order in A344023. (End)
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LINKS
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FORMULA
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a(p^k) = p for p prime and k>=1.
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EXAMPLE
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a(60) = 136 because the distinct prime factors of 60 are {2, 3, 5} and 2^1 + 3^2 + 5^3 = 136.
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MATHEMATICA
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{0}~Join~Table[Total[(a=First/@FactorInteger[k])^Range@Length@a], {k, 2, 100}]
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PROG
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(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, f[k, 1]^k); \\ Michel Marcus, Apr 11 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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