A167353 Totally multiplicative sequence with a(p) = (p+1)*(p+3) = p^2+4p+3 for prime p.

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

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