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Search: id:A069088
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| A069088 |
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Sum(d|n, core(d) ) where d are the divisors of n and where core(d) is the square-free part of d: the smallest number such that d*core(d) is a square. |
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+0
2
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| 1, 3, 4, 4, 6, 12, 8, 6, 5, 18, 12, 16, 14, 24, 24, 7, 18, 15, 20, 24, 32, 36, 24, 24, 7, 42, 8, 32, 30, 72, 32, 9, 48, 54, 48, 20, 38, 60, 56, 36, 42, 96, 44, 48, 30, 72, 48, 28, 9, 21, 72, 56, 54, 24, 72, 48, 80, 90, 60, 96, 62, 96, 40, 10, 84, 144, 68, 72, 96, 144, 72, 30, 74
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Multiplicative because it is the Inverse Moebius transform of A007913 which is multiplicative. Christian G. Bower (bowerc(AT)usa.net) May 17, 2005.
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FORMULA
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G.f.: sum(k>=1, core(k)*x^k/(1-x^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2003
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PROGRAM
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(PARI) for(n=1, 120, print1(sumdiv(n, d, core(d)), ", "))
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CROSSREFS
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Cf. A007913.
Sequence in context: A089640 A086659 A008473 this_sequence A019462 A078071 A084138
Adjacent sequences: A069085 A069086 A069087 this_sequence A069089 A069090 A069091
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KEYWORD
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easy,nonn,mult
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 05 2002
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