id:A161148 - OEIS Search Results

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Number of partitions of n such that each term of the partition is a squared divisor of n.

+0
1

1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 5, 1, 4, 2, 6, 1, 9, 1, 8, 3, 6, 1, 16, 2, 7, 4, 12, 1, 21, 1, 15, 4, 9, 2, 39, 1, 10, 5, 25, 1, 35, 1, 24, 9, 12, 1, 76, 2, 21, 6, 32, 1, 61, 3, 38, 7, 15, 1, 174, 1, 16, 10, 46, 3, 93, 1, 50, 8, 42, 1, 231, 1, 19, 19, 60, 2, 135, 1 (list; graph; listen)

	OFFSET	`1,4`
	FORMULA	`a(p)=1 if p a prime (A000040). a(2p)=A130291(n) if p=A000040(n). a(n) = [x^n] product_{d\|n} 1/( 1-x^(d^2) ).`
	EXAMPLE	`a(n=12)=5 counts these 5 partitions of 12: 1^2+1^2+..+1^2 = 1^2+1^2+...+1^2+2^2 = 1^2+1^2+..+1^2+2^2+2^2 = 1^2+1^2+1^2+3^2=2^2+2^2+2^2. Partitions with the divisors 4, 6 or 12 do not contribute to the count because 4^2, 6^2 and 12^2 are larger than n.`
	MAPLE	`a := proc(n) coeftayl(1/mul(1-x^(d^2), d=numtheory[divisors](n)), x=0, n) ; end:`
	CROSSREFS	`Cf. A018818, A001156, A002635.` `Sequence in context: A160006 A060682 A093873 this_sequence A143773 A053279 A046800` `Adjacent sequences: A161145 A161146 A161147 this_sequence A161149 A161150 A161151`
	KEYWORD	`nonn`
	AUTHOR	`R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 03 2009`

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.

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