id:A100073 - OEIS Search Results

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Number of representations of n as the difference of two positive squares.

+0
1

0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 1, 2, 1, 0, 2, 1, 1, 0, 1, 2, 2, 0, 2, 1, 1, 0, 2, 2, 1, 0, 1, 1, 3, 0, 1, 3, 1, 0, 2, 1, 1, 0, 2, 2, 2, 0, 1, 2, 1, 0, 3, 2, 2, 0, 1, 1, 2, 0, 1, 3, 1, 0, 3, 1, 2, 0, 1, 3, 2, 0, 1, 2, 2, 0, 2, 2, 1, 0, 2, 1, 2, 0, 2, 4, 1, 0, 3, 1, 1, 0, 1, 2, 4 (list; graph; listen)

	OFFSET	`1,15`
	COMMENT	`Note that for odd n, a(n) = 1 iff n is a prime, or a prime squared.`
	FORMULA	`a(n) = A056924(n) for odd n, a(n) = A056924(n/4) if 4\|n, otherwise a(n) = 0.`
	EXAMPLE	`a(15) = 2 because 15 = 16-1 = 64-49.`
	MATHEMATICA	`nn=150; a=Table[0, {nn}]; Do[y=x-1; While[d=x^2-y^2; d<=nn&&y>0, a[[d]]++; y-- ], {x, 1+nn/2}]; a`
	CROSSREFS	`Cf. A056924 (number of divisors of n that are less than sqrt(n)), A016825 (numbers not the difference of two squares), A034178 (number of representations of n as the difference of two squares).` `Adjacent sequences: A100070 A100071 A100072 this_sequence A100074 A100075 A100076` `Sequence in context: A026920 A060763 A131576 this_sequence A075685 A037906 A120936`
	KEYWORD	`easy,nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Nov 02 2004`

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Last modified November 9 12:23 EST 2009. Contains 166233 sequences.

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