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A118585
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Sum of squares of digits of prime factors of n, with multiplicity.
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0
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0, 4, 9, 8, 25, 13, 49, 12, 18, 29, 2, 17, 10, 53, 34, 16, 50, 22, 82, 33, 58, 6, 13, 21, 50, 14, 27, 57, 85, 38, 10, 20, 11, 54, 74, 26, 58, 86, 19, 37, 17, 62, 25, 10, 43, 17, 65, 25, 98, 54, 59, 18, 34, 31, 27, 61, 91, 89, 106, 42
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OFFSET
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1,2
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COMMENTS
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Differs from A067666 if any prime factor exceeds 1 digit. Fixed points include 16, 27. See also: A067666 Sum of squares of prime factors of n (counted with multiplicity). See also: A003132 Sum of squares of digits of n. See also: A118503 Sum of digits of prime factors of n, with multiplicity.
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LINKS
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FORMULA
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a(n) = SUM[i=1..k] (e_i)*A003132(p_i) where prime decomposition of n = (p_1)^(e_1) * (p_2)^(e_2) * ... * (p_k)^(e_k).
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EXAMPLE
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a(22) = 6 because 22 = 2 * 11 and the sum of squares of digits of prime factors is 2^2 + 1^2 + 1^2.
a(121) = 4 because 121 = 11^2 = 11 * 11, so 1^2 + 1^2 + 1^2 + 1^2 = 4.
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MATHEMATICA
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Join[{0}, Table[Total[Flatten[IntegerDigits/@(Flatten[Table[#[[1]], #[[2]]]&/@ FactorInteger[ n]])]^2], {n, 2, 60}]] (* Harvey P. Dale, Nov 17 2022 *)
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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