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A018818
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Number of partitions of n into divisors of n.
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16
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1, 2, 2, 4, 2, 8, 2, 10, 5, 11, 2, 45, 2, 14, 14, 36, 2, 81, 2, 92, 18, 20, 2, 458, 7, 23, 23, 156, 2, 742, 2, 202, 26, 29, 26, 2234, 2, 32, 30, 1370, 2, 1654, 2, 337, 286, 38, 2, 9676, 9, 407, 38, 454, 2, 3132, 38, 3065, 42, 47, 2, 73155, 2, 50, 493, 1828, 44, 5257, 2, 740, 50, 5066
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Quite trivial, but a(n) = 2 iff n is prime. [From Juhani Heino (Juhani.Heino(AT)sanasepot.fi), Aug 27 2009]
Contribution from Reinhard Zumkeller, Dec 11 2009: (Start)
For odd primes p: a(p^2) = p + 2; for n>1: a(A001248(n))=A052147(n);
for odd primes p>3: a(3*p) = 2*p + 4; for n>2: a(A001748(n))=A100484(n)+4. (End)
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REFERENCES
| H. Gupta, Partitions of n into divisors of m, Indian J. Pure Appl. Math. 6 (1975), no. 11, 1276-1286.
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LINKS
| Alois P. Heinz and T. D. Noe, Table of n, a(n) for n = 1..10000 [Terms 1 through 1000 were computed by T. D. Noe, terms 1001 through 1000 by A. P. Heinz]
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FORMULA
| Coefficient of x^n in expansion of 1/Product_{d divides n} (1-x^d). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 28 2002
a(n) = f(n,n,1) with f(n,m,k) = if k<=m then f(n,m,k+1)+f(n,m-k,k)*0^(n mod k) else 0^m. [From Reinhard Zumkeller, Dec 11 2009]
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MATHEMATICA
| Table[d = Divisors[n]; Coefficient[Series[1/Product[1 - x^d[[i]], {i, Length[d]}], {x, 0, n}], x, n], {n, 100}] (* T. D. Noe, Jul 28 2011 *)
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CROSSREFS
| Cf. A002577.
Cf. A033630, A171565. [From Reinhard Zumkeller, Dec 11 2009]
Sequence in context: A072478 A190014 A100577 * A157019 A067538 A096154
Adjacent sequences: A018815 A018816 A018817 * A018819 A018820 A018821
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KEYWORD
| nonn,nice
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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