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A254520 Möbius transform of A034676. 1
1, 4, 9, 12, 25, 36, 49, 48, 72, 100, 121, 108, 169, 196, 225, 192, 289, 288, 361, 300, 441, 484, 529, 432, 600, 676, 648, 588, 841, 900, 961, 768, 1089, 1156, 1225, 864, 1369, 1444, 1521, 1200, 1681, 1764, 1849, 1452, 1800, 2116, 2209, 1728, 2352, 2400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Dirichlet convolution of a(n) and sigma(n) is sigma(n^2).

LINKS

Álvar Ibeas, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = n^2 * Sum_{d^2 | n} (moebius(d) / d^2).

Multiplicative with a(p) = p^2; a(p^e) = p^(2e) - p^(2e-2), for e > 1.

Dirichlet g.f.: zeta(s-2) / zeta(2s-2).

Sum_{k=1..n} a(k) ~ 30 * n^3 / Pi^4. - Vaclav Kotesovec, Jan 11 2019

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/p^2 + 1/(p^2 - 1)^2) = 1.681923034881403168503816690236967736500606659628336043348190538886262268... - Vaclav Kotesovec, Sep 20 2020

PROG

(PARI) a(n) = n^2*sumdiv(n, d, if (issquare(d), moebius(sqrtint(d))/d)); \\ Michel Marcus, Feb 10 2015

CROSSREFS

Cf. A000290, A000203, A034676, A065764.

Sequence in context: A344415 A297414 A076794 * A344578 A283105 A179808

Adjacent sequences:  A254517 A254518 A254519 * A254521 A254522 A254523

KEYWORD

mult,nonn

AUTHOR

Álvar Ibeas, Jan 31 2015

STATUS

approved

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Last modified January 18 00:56 EST 2022. Contains 350410 sequences. (Running on oeis4.)