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A071785
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In prime factorization of n replace each prime with the sum of its decimal digits.
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1
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 12, 4, 14, 15, 16, 8, 18, 10, 20, 21, 4, 5, 24, 25, 8, 27, 28, 11, 30, 4, 32, 6, 16, 35, 36, 10, 20, 12, 40, 5, 42, 7, 8, 45, 10, 11, 48, 49, 50, 24, 16, 8, 54, 10, 56, 30, 22, 14, 60, 7, 8, 63, 64, 20, 12, 13, 32, 15, 70, 8, 72
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OFFSET
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1,2
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LINKS
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FORMULA
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Multiplicative with a(p) = A007953(p), p prime.
a(n) = n iff n is 7-smooth (A002473).
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EXAMPLE
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a(143) = a(11*13) = a(11)*a(13) = (1+1)*(1+3) = 2*4 = 8.
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MAPLE
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a:= n-> mul(add(j, j=convert(i[1], base, 10))^i[2], i=ifactors(n)[2]):
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MATHEMATICA
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a[n_] := Product[{p, e} = pe; Total[IntegerDigits[p]]^e, {pe, FactorInteger[n]}];
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PROG
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(PARI) a(n, base=10) = my (f=factor(n)); prod(i=1, #f~, sumdigits(f[i, 1], base)^f[i, 2]) \\ Rémy Sigrist, Feb 19 2019
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CROSSREFS
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KEYWORD
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nonn,base,mult
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AUTHOR
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STATUS
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approved
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