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A057670
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Sum [LCM(k, n/k)], where sum is over positive integers k that divide n.
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2
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1, 4, 6, 10, 10, 24, 14, 24, 21, 40, 22, 60, 26, 56, 60, 52, 34, 84, 38, 100, 84, 88, 46, 144, 55, 104, 72, 140, 58, 240, 62, 112, 132, 136, 140, 210, 74, 152, 156, 240, 82, 336, 86, 220, 210, 184, 94, 312, 105, 220, 204, 260, 106, 288, 220, 336, 228, 232, 118, 600
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OFFSET
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1,2
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COMMENTS
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Multiplicative with a(p^e) = sum p^max(k, e-k), k=0..e (Cf. A107661). Mitch Harris May 18, 2005.
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LINKS
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Table of n, a(n) for n=1..60.
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FORMULA
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Multiplicative with a(p) = 2*p, a(p^k) = (2*p^(k+1) - p^ceiling[(k+1)/2] - p^floor[(k+1)/2]) / (p-1). a(n) is odd iff n is an odd square. - Henry Bottomley, May 16 2005
Dirichlet g.f. (zeta(s-1))^2*zeta(2s-1)/zeta(2s-2). - R. J. Mathar, Feb 11 2011
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EXAMPLE
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a(8) = LCM(1,8) + LCM(2,4) + LCM(4,2) + LCM(8,1) = 8 + 4 + 4 + 8 = 24.
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CROSSREFS
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Cf. A055155.
Sequence in context: A088682 A102415 A117003 * A171615 A141780 A185002
Adjacent sequences: A057667 A057668 A057669 * A057671 A057672 A057673
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KEYWORD
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nonn,mult
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AUTHOR
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Leroy Quet Oct 18 2000
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STATUS
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approved
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