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A193553 Sum of divisors of 4*n. 16
7, 15, 28, 31, 42, 60, 56, 63, 91, 90, 84, 124, 98, 120, 168, 127, 126, 195, 140, 186, 224, 180, 168, 252, 217, 210, 280, 248, 210, 360, 224, 255, 336, 270, 336, 403, 266, 300, 392, 378, 294, 480, 308, 372, 546, 360, 336, 508, 399, 465, 504, 434, 378, 600, 504, 504, 560, 450, 420, 744, 434, 480, 728, 511, 588, 720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = sigma(4*n) = A000203(4*n).

a(n) = 3*sigma(2*n) - 2*sigma(n); the relation is the special case e=1, p=2 of the relation sigma(t^2*n) = (t+1)*sigma(t*n) - t*sigma(n) where t=p^e (p a prime).

G.f. is x times the logarithmic derivative of the g.f. of A182820.

a(2*n-1) = 7 * A008438(n) = 7 * sigma(2*n-1); special case of sigma(2^k*(2*n-1)) = (2^(k+1)-1) * sigma(2*n-1).

MATHEMATICA

DivisorSigma[1, 4*Range[70]] (* Harvey P. Dale, Jan 27 2015 *)

PROG

(PARI) vector(66, n, sigma(4*n, 1))

CROSSREFS

Sigma(k*n): A000203 (k=1), A062731 (k=2), A144613 (k=3), this sequence (k=4), A224613 (k=6), A283078 (k=7).

Sequence in context: A292379 A146624 A239934 * A274090 A195041 A229462

Adjacent sequences:  A193550 A193551 A193552 * A193554 A193555 A193556

KEYWORD

nonn

AUTHOR

Joerg Arndt, Jul 30 2011

STATUS

approved

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Last modified October 14 04:35 EDT 2019. Contains 327995 sequences. (Running on oeis4.)