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Search: id:A093811
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| A093811 |
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Sum of the digital products of the divisors of n. |
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+0
2
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| 1, 3, 4, 7, 6, 12, 8, 15, 13, 8, 2, 18, 4, 14, 14, 21, 8, 29, 10, 12, 13, 8, 7, 34, 16, 18, 27, 34, 19, 22, 4, 27, 14, 22, 28, 53, 22, 36, 34, 20, 5, 33, 13, 28, 43, 33, 29, 72, 44, 18, 16, 32, 16, 63, 32, 72, 48, 61, 46, 28, 7, 18, 40, 51, 39, 62, 43, 74, 64, 34, 8, 83, 22, 52, 59
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The first few n such that a(n) = n are: 1,14,27,156,196. Are there any more?
Inverse Moebius transform of A007954(n). a(n) = A007954(n) * A000012(n), where operation * denotes Dirichlet convolution for n >= 1. Dirichlet convolution of functions b(n), c(n) is function a(n) = b(n) * c(n) = Sum_{d|n} b(d)*c(n/d). Simultaneously holds Dirichlet multiplication: a(n) * A008683(n) = A007954(n). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 22 2009]
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EXAMPLE
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a(1234)=69 because the divisors of 1234 are: [1, 2, 617, 1234] and
1+2+(6*1*7)+(1*2*3*4) = 69.
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CROSSREFS
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Cf. A007954, A008683, A000012. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 22 2009]
Sequence in context: A051378 A116607 A107749 this_sequence A088000 A034690 A069192
Adjacent sequences: A093808 A093809 A093810 this_sequence A093812 A093813 A093814
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), May 20 2004
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