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A020487

Antiharmonic numbers: numbers n such that sigma_1(n) divides sigma_2(n).

+0
9

1, 4, 9, 16, 20, 25, 36, 49, 50, 64, 81, 100, 117, 121, 144, 169, 180, 196, 200, 225, 242, 256, 289, 324, 325, 361, 400, 441, 450, 468, 484, 500, 529, 576, 578, 605, 625, 650, 676, 729, 784, 800, 841, 900, 961, 968, 980, 1024, 1025, 1058, 1089, 1156, 1225, 1280, 1296 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`Numbers k such that antiharmonic mean of divisors of k is an integer. Antiharmonic mean of divisors of number m = Product (p_i^e_i) is A001157(m)/A000203(m) = Product ((p_i^(e_i+1)+1)/(p_i+1)). a(n) = k = A001157(k)/A000203(k) for A001157(k)/A000203(k)is integer. (jaroslav.krizek(AT)atlas.cz) [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 09 2009]`
	EXAMPLE	`For n=3 the a(3)=9=3^2, antiharmonic mean of divisors of number 9 is (3^(2+1)+1)/(3+1)=7, 7 is integer. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 09 2009]`
	CROSSREFS	`Cf. A001157, A000203. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 09 2009]` `Sequence in context: A066213 A010441 A046871 this_sequence A046870 A010461 A010421` `Adjacent sequences: A020484 A020485 A020486 this_sequence A020488 A020489 A020490`
	KEYWORD	`nonn`
	AUTHOR	`David W. Wilson (davidwwilson(AT)comcast.net)`

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Last modified December 16 17:18 EST 2009. Contains 170825 sequences.

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