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A167353 Totally multiplicative sequence with a(p) = (p+1)*(p+3) = p^2+4p+3 for prime p. 1
1, 15, 24, 225, 48, 360, 80, 3375, 576, 720, 168, 5400, 224, 1200, 1152, 50625, 360, 8640, 440, 10800, 1920, 2520, 624, 81000, 2304, 3360, 13824, 18000, 960, 17280, 1088, 759375, 4032, 5400, 3840, 129600, 1520, 6600, 5376, 162000, 1848, 28800 (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+3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)*(p(k)+3))^e(k). a(n) = A003959(n) * A166591(n).

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 4*p + 2)) = 1.1854020769112984236586594287311260820805752130814044791625914047437286210... - Vaclav Kotesovec, Sep 20 2020

MATHEMATICA

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^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 11 2016 *)

CROSSREFS

Cf. A003959, A166591.

Sequence in context: A154150 A324484 A167709 * A219880 A216379 A120746

Adjacent sequences:  A167350 A167351 A167352 * A167354 A167355 A167356

KEYWORD

nonn,mult

AUTHOR

Jaroslav Krizek, Nov 01 2009

STATUS

approved

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Last modified April 11 21:23 EDT 2021. Contains 342888 sequences. (Running on oeis4.)