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Search: id:A118585
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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
1
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| 0, 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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Differs from A067666 if any prime factor exceeds 1 digit. Fixed points include 11, 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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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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CROSSREFS
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Cf. A001221, A001222, A003132, A007953, A007954, A067666, A095402, A118503.
Sequence in context: A063748 A121920 A065642 this_sequence A067666 A050399 A072995
Adjacent sequences: A118582 A118583 A118584 this_sequence A118586 A118587 A118588
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), May 07 2006
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