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A062370 a(n) = Sum_{i|n,j|n} sigma(i)*sigma(j)/sigma(gcd(i,j)), where sigma(n) = sum of divisors of n. 1
1, 10, 13, 45, 19, 130, 25, 150, 78, 190, 37, 585, 43, 250, 247, 429, 55, 780, 61, 855, 325, 370, 73, 1950, 174, 430, 358, 1125, 91, 2470, 97, 1122, 481, 550, 475, 3510, 115, 610, 559, 2850, 127, 3250, 133, 1665, 1482, 730, 145, 5577, 310, 1740, 715, 1935 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(p^e) = 1 + Sum_{k=1..e} (2k+1)sigma(p^k). - Mitch Harris, May 24 2005

a(n) = Sum_{d|n} tau(d^2)*sigma(d), where tau(k) = A000005(k) and sigma(k) = A000203(k). - Ridouane Oudra, Aug 25 2019

MAPLE

with(numtheory): seq(add(tau(d^2)*sigma(d), d in divisors(n)), n=1..60); # Ridouane Oudra, Aug 25 2019

MATHEMATICA

a[n_] := DivisorSum[n, DivisorSigma[0, #^2] * DivisorSigma[1, #] &]; Array[a, 100] (* Amiram Eldar, Sep 15 2019 *)

PROG

(PARI) a(n) = my(f=factor(n)); for (j=1, #f~, f[j, 1] = 1+ sum(k=1, f[j, 2], (2*k+1)*sigma(f[j, 1]^k)); f[j, 2] = 1); factorback(f); \\ Michel Marcus, Feb 28 2019

CROSSREFS

Cf. A000203, A060648, A000005.

Sequence in context: A102249 A195313 A219829 * A069960 A219715 A154142

Adjacent sequences:  A062367 A062368 A062369 * A062371 A062372 A062373

KEYWORD

nonn,mult

AUTHOR

Vladeta Jovovic, Jul 07 2001

STATUS

approved

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Last modified March 6 20:37 EST 2021. Contains 341850 sequences. (Running on oeis4.)