The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A338547 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A338547

a(n) = n^2 * Sum_{d|n} (-1)^(n/d + 1) * mu(d) / d^2.
(history; published version)

#13 by Peter Luschny at Wed Nov 16 06:55:49 EST 2022

STATUS

reviewed

approved

#12 by Michel Marcus at Wed Nov 16 03:34:17 EST 2022

STATUS

proposed

reviewed

#11 by Amiram Eldar at Tue Nov 15 17:35:57 EST 2022

STATUS

editing

proposed

#10 by Amiram Eldar at Tue Nov 15 15:48:55 EST 2022

FORMULA

Multiplicative with a(2) = -5, a(2^e) = -3*2^(2*(e-1)), for e > 1, and a(p^e) = (p^2-1)*p^(2*(e-1)) for p > 2. - Amiram Eldar, Nov 15 2022

#9 by Amiram Eldar at Tue Nov 15 15:47:45 EST 2022

LINKS

Amiram Eldar, <a href="/A338547/b338547.txt">Table of n, a(n) for n = 1..10000</a>

FORMULA

Multiplicative with a(2) = -5, a(2^e) = -3*2^(2*(e-1)), and a(p^e) = (p^2-1)*p^(2*(e-1)) for p > 2. - Amiram Eldar, Nov 15 2022

MATHEMATICA

f[p_, e_] := (p^2 - 1)*p^(2*(e - 1)); f[2, 1] = -5; f[2, e_] := -3*2^(2*(e - 1)); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 15 2022 *)

STATUS

approved

editing

#8 by Susanna Cuyler at Mon Nov 02 20:36:52 EST 2020

STATUS

proposed

approved

#7 by Michel Marcus at Mon Nov 02 10:17:44 EST 2020

STATUS

editing

proposed

#6 by Michel Marcus at Mon Nov 02 10:17:40 EST 2020

PROG

(PARI) a(n) = n^2 * sumdiv(n, d, (-1)^(n/d+1)*moebius(d)/d^2); \\ Michel Marcus, Nov 02 2020

STATUS

proposed

editing

#5 by Ilya Gutkovskiy at Mon Nov 02 10:05:44 EST 2020

STATUS

editing

proposed

#4 by Ilya Gutkovskiy at Mon Nov 02 09:50:01 EST 2020

CROSSREFS

Cf. A007434, A008683, A162395, A321543, A325596, A338548, A338549.