A167340 Totally multiplicative sequence with a(p) = p*(p+2) = p^2+2p for prime p.

1, 8, 15, 64, 35, 120, 63, 512, 225, 280, 143, 960, 195, 504, 525, 4096, 323, 1800, 399, 2240, 945, 1144, 575, 7680, 1225, 1560, 3375, 4032, 899, 4200, 1023, 32768, 2145, 2584, 2205, 14400, 1443, 3192, 2925, 17920, 1763, 7560, 1935, 9152, 7875, 4600

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (p*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)+2))^e(k). a(n) = n * A166590(n).

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 2*p - 1)) = 1.316691699195895375836915424544566393355705508235453271181975628362968836... - Vaclav Kotesovec, Sep 20 2020

Mathematica

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

Crossrefs

Sequence in context: A151792 A243295 A118526 * A037377 A166704 A161342

Adjacent sequences: A167337 A167338 A167339 * A167341 A167342 A167343

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved