id:A143348 - OEIS Search Results

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a(n) = -(-1)^n times sum of divisors of n.

+0
2

1, -3, 4, -7, 6, -12, 8, -15, 13, -18, 12, -28, 14, -24, 24, -31, 18, -39, 20, -42, 32, -36, 24, -60, 31, -42, 40, -56, 30, -72, 32, -63, 48, -54, 48, -91, 38, -60, 56, -90, 42, -96, 44, -84, 78, -72, 48, -124, 57, -93, 72, -98, 54, -120, 72, -120, 80, -90, 60, -168, 62, -96, 104, -127, 84, -144, 68, -126, 96 (list; graph; listen)

	OFFSET	`1,2`
	FORMULA	`a(n) is multiplicative with a(2^e) = 1 - 2^(e+1) if e>0, a(p^e) = (p^(e+1) - 1) / (p - 1) if p>2.` `G.f.: Sum_{k>0} k * -(-x)^k / (1 - (-x)^k) = Sum_{k>0} -(-x)^k / (1 - (-x)^k)^2.` `Dirichlet g.f.: zeta(s) * zeta(s-1) * (1 - 6 / 2^s + 4 / 4^s).`
	EXAMPLE	`q - 3q^2 + 4q^3 - 7q^4 + 6q^5 - 12q^6 + 8q^7 - 15q^8 + 13q^9 + ...`
	PROGRAM	`(PARI) {a(n) = if( n<1, 0, -(-1)^n * sigma(n))}`
	CROSSREFS	`-(-1)^n * A000203(n) = a(n). A143337(n) = 24 * a(n) unless n=0.` `Sequence in context: A074847 A097863 A097012 this_sequence A000203 A003979 A084250` `Adjacent sequences: A143345 A143346 A143347 this_sequence A143349 A143350 A143351`
	KEYWORD	`sign,mult`
	AUTHOR	`Michael Somos, Aug 09 2008`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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