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A167344 Totally multiplicative sequence with a(p) = (p-1)*(p+1) = p^2-1 for prime p. 5
1, 3, 8, 9, 24, 24, 48, 27, 64, 72, 120, 72, 168, 144, 192, 81, 288, 192, 360, 216, 384, 360, 528, 216, 576, 504, 512, 432, 840, 576, 960, 243, 960, 864, 1152, 576, 1368, 1080, 1344, 648, 1680, 1152, 1848, 1080, 1536, 1584, 2208, 648, 2304, 1728 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

Multiplicative with a(p^e) = ((p-1)*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)*(p(k)+1))^e(k).

a(n) = A003958(n) * A003959(n).

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 - 2)) = 1.884261780923861906728291280746835210118330549695678826316037127832097567... - Vaclav Kotesovec, Sep 20 2020

a(n) = A340323(n) * A340368(n). - Antti Karttunen, Jan 31 2021

MATHEMATICA

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 1)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 10 2016 *)

PROG

(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = f[k, 1]^2-1); factorback(f); \\ Michel Marcus, Jan 31 2021

CROSSREFS

Cf. A003958, A003959, A306709, A340323, A340368.

Cf. also A335915.

Sequence in context: A191487 A176205 A099256 * A025615 A297324 A223331

Adjacent sequences:  A167341 A167342 A167343 * A167345 A167346 A167347

KEYWORD

nonn,mult

AUTHOR

Jaroslav Krizek, Nov 01 2009

STATUS

approved

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Last modified April 11 00:03 EDT 2021. Contains 342877 sequences. (Running on oeis4.)