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A053051
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Smallest integer m such that sum_(k=1 to m) d(k) is divisible by n, where d(k) (A000005) is the number of divisors of k.
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1
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1, 4, 2, 4, 3, 19, 6, 4, 10, 5, 20, 19, 17, 6, 15, 7, 32, 48, 23, 8, 24, 20, 9, 42, 16, 17, 10, 24, 11, 19, 46, 41, 20, 43, 12, 164, 13, 23, 63, 41, 14, 24, 76, 44, 15, 80, 47, 108, 67, 16, 96, 17, 109, 164, 121, 42, 86, 18, 89, 19, 132, 46, 235, 149, 150, 20, 49, 281, 50
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Matthew M. Conroy, Home page (listed instead of email address)
M. L. Perez et al., eds., Smarandache Notions Journal
F. Russo, A set of new Smarandache functions, sequences and conjectures in number theory.
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EXAMPLE
| a(1)=1 since 1 has 1 divisor; a(3)=2 since 1 has 1 divisor, 2 has 2 divisors and 1+2=3; a(2)=4 since 1+2+2+3=8, a multiple of 4, while 1, 1+2 and 1+2+2 are not multiples of 4.
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MATHEMATICA
| a[n_] := (m = 1; While[ !Divisible[ Sum[ DivisorSigma[0, k], {k, 1, m}], n], m++]; m); Table[ a[n], {n, 1, 69}] (* From Jean-François Alcover, Dec 28 2011 *)
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CROSSREFS
| Cf. A000005, A002034, A011772, A006218.
Sequence in context: A083954 A038702 A085062 * A075234 A095382 A135282
Adjacent sequences: A053048 A053049 A053050 * A053052 A053053 A053054
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Felice Russo (frusso(AT)micron.com), Feb 25 2000
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EXTENSIONS
| More terms from Matthew M. Conroy, May 13 2001
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