A167363 Totally multiplicative sequence with a(p) = (p+3)^2 = p^2+6p+9 for prime p.

1, 25, 36, 625, 64, 900, 100, 15625, 1296, 1600, 196, 22500, 256, 2500, 2304, 390625, 400, 32400, 484, 40000, 3600, 4900, 676, 562500, 4096, 6400, 46656, 62500, 1024, 57600, 1156, 9765625, 7056, 10000, 6400, 810000, 1600, 12100, 9216, 1000000, 1936, 90000

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = ((p+3)^2)^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+3)^2)^e(k). a(n) = A166591(n)^2.

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 6*p + 8)) = 1.1245403934230393267573507658470307221064356442604979888687782305037985824... - Vaclav Kotesovec, Sep 20 2020

Mathematica

b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[b[n]^2, {n, 1, 100}] (* G. C. Greubel, Jun 11 2016 *)

Crossrefs

Cf. A166591.

Sequence in context: A077676 A030671 A030681 * A035383 A179803 A061863

Adjacent sequences: A167360 A167361 A167362 * A167364 A167365 A167366

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved