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

Author

Jaroslav Krizek, Nov 01 2009

Keywords

• nonn
• mult

Links

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

Crossrefs

Cf. A003959, A166591.

Programs

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 *)

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