A167358 Totally multiplicative sequence with a(p) = (p+2)^2 = p^2+4p+4 for prime p.

1, 16, 25, 256, 49, 400, 81, 4096, 625, 784, 169, 6400, 225, 1296, 1225, 65536, 361, 10000, 441, 12544, 2025, 2704, 625, 102400, 2401, 3600, 15625, 20736, 961, 19600, 1089, 1048576, 4225, 5776, 3969, 160000, 1521, 7056, 5625, 200704, 1849, 32400, 2025, 43264

Offset

1,2

Links

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

Formula

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

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 4*p + 3)) = 1.1773018966974266400752906612246691227245078032189833736353235503076639420... - 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]^2, {n, 1, 100}] (* G. C. Greubel, Jun 11 2016 *)

Crossrefs

Cf. A166590.

Sequence in context: A260047 A061101 A166672 * A267764 A264588 A291093

Adjacent sequences: A167355 A167356 A167357 * A167359 A167360 A167361

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved