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A062367 Multiplicative with a(p^e) = (e+1)*(e+2)*(2*e+3)/6. 4
1, 5, 5, 14, 5, 25, 5, 30, 14, 25, 5, 70, 5, 25, 25, 55, 5, 70, 5, 70, 25, 25, 5, 150, 14, 25, 30, 70, 5, 125, 5, 91, 25, 25, 25, 196, 5, 25, 25, 150, 5, 125, 5, 70, 70, 25, 5, 275, 14, 70, 25, 70, 5, 150, 25, 150, 25, 25, 5, 350, 5, 25, 70, 140, 25, 125, 5, 70, 25, 125, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

Also a(n) = Sum_{i|n, j|n} tau(gcd(i, j)) = Sum_{d|n} tau(d)^2.

a(n) = Sum_{i|n, j|n} tau(i)*tau(j)/tau(lcm(i, j)), where tau(n) = number of divisors of n, cf. A000005.

Dirichlet convolution of A035116 and A000012 (i.e., inverse Mobius transform of A035116). Dirichlet g.f.: zeta^5(s)/zeta(2s). - R. J. Mathar, Feb 03 2011

G.f.: Sum_{n>=1} A000005(n)^2*x^n/(1-x^n). - Mircea Merca, Feb 26 2014

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(tau(k)^2/k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 23 2018

Dirichlet convolution of A007426 and A008966. Dirichlet convolution of A007425 and A034444. - R. J. Mathar, Jun 05 2020

PROG

(PARI) a(n) = sumdiv(n, d, numdiv(d)^2) \\ Michel Marcus, Jun 17 2013

CROSSREFS

Cf. A000005, A000012, A000330, A029939, A035116, A060648, A062368.

Sequence in context: A076903 A192987 A252768 * A286257 A168418 A266440

Adjacent sequences:  A062364 A062365 A062366 * A062368 A062369 A062370

KEYWORD

nonn,mult

AUTHOR

Vladeta Jovovic, Jul 07 2001

STATUS

approved

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Last modified September 29 21:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)