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A322360 Multiplicative with a(p^e) = (p^2)-1. 3
1, 3, 8, 3, 24, 24, 48, 3, 8, 72, 120, 24, 168, 144, 192, 3, 288, 24, 360, 72, 384, 360, 528, 24, 24, 504, 8, 144, 840, 576, 960, 3, 960, 864, 1152, 24, 1368, 1080, 1344, 72, 1680, 1152, 1848, 360, 192, 1584, 2208, 24, 48, 72, 2304, 504, 2808, 24, 2880, 144, 2880, 2520, 3480, 576, 3720, 2880, 384, 3, 4032, 2880 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Absolute values of A046970, the Dirichlet inverse of the Jordan function J_2 (A007434).

Absolute values of the Möbius transform of A055491. (See Benoit Cloitre's May 31 2002 comment in A046970).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(p^e) = (p^2)-1.

a(n)) = Product_{p prime divides n} (p^2 - 1).

a(n) = abs(A046970(n)).

a(n) = A048250(n) * A173557(n) = A066086(n) * A322359(n).

MATHEMATICA

a[n_] := If[n==1, 1, Times @@ ((#^2-1)& @@@ FactorInteger[n])]; Array[a, 50]  (* Amiram Eldar, Dec 05 2018 *)

PROG

(PARI) A322360(n) = factorback(apply(p -> (p*p)-1, factor(n)[, 1]));

(PARI) A322360(n) = abs(sumdiv(n, d, moebius(n/d)*(core(d)^2)));

CROSSREFS

Absolute values of A046970.

Cf. A048250, A173557, A066086, A322359.

Sequence in context: A220138 A146975 A046970 * A058936 A280369 A280979

Adjacent sequences:  A322357 A322358 A322359 * A322361 A322362 A322363

KEYWORD

nonn,mult

AUTHOR

Antti Karttunen, Dec 04 2018

STATUS

approved

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Last modified April 19 01:29 EDT 2019. Contains 322237 sequences. (Running on oeis4.)