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A073185
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Sum of cube-free divisors of n.
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4
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1, 3, 4, 7, 6, 12, 8, 7, 13, 18, 12, 28, 14, 24, 24, 7, 18, 39, 20, 42, 32, 36, 24, 28, 31, 42, 13, 56, 30, 72, 32, 7, 48, 54, 48, 91, 38, 60, 56, 42, 42, 96, 44, 84, 78, 72, 48, 28, 57, 93, 72, 98, 54, 39, 72, 56, 80, 90, 60, 168, 62, 96, 104, 7, 84, 144, 68, 126, 96, 144, 72
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) = sum of divisors of the cube-free kernel of n: a(n)=A000203(A007948(n));
a(n) <= A073183(n).
Multiplicative because it is the Dirichlet convolution of a(n)=n with characteristic function of cube-free numbers, both multiplicative sequences. a(p) = 1+p, a(p^e) = 1+p+p^2, e>1. Christian G. Bower (bowerc(AT)usa.net) May 18, 2005.
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FORMULA
| Dirichlet g.f. zeta(s)*zeta(s-1)/zeta(3s-3). - R. J. Mathar, Apr 12 2011
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EXAMPLE
| The divisors of 56 are {1, 2, 4, 7, 8, 14, 28, 56}, 8=2^3 and 56=7*2^3 are not cube-free, therefore a(56)=1+2+4+7+14+28=56. [ !?]
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MAPLE
| charFfree := proc(n, t) local f; for f in ifactors(n)[2] do if op(2, f) >= t then return 0 ; end if; end do: return 1 ; end proc:
A073185 := proc(n) add( d*charFfree(d, 3), d =numtheory[divisors](n) ); end proc: # R. J. Mathar, Apr 12 2011
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CROSSREFS
| Cf. A000203, A073184, A004709, A073182, A073181, A048250.
Sequence in context: A126253 A057032 A113957 * A073183 A049418 A051378
Adjacent sequences: A073182 A073183 A073184 * A073186 A073187 A073188
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KEYWORD
| nonn,mult
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 19 2002
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