A167342 Totally multiplicative sequence with a(p) = p*(p+3) = p^2+3p for prime p.

1, 10, 18, 100, 40, 180, 70, 1000, 324, 400, 154, 1800, 208, 700, 720, 10000, 340, 3240, 418, 4000, 1260, 1540, 598, 18000, 1600, 2080, 5832, 7000, 928, 7200, 1054, 100000, 2772, 3400, 2800, 32400, 1480, 4180, 3744, 40000, 1804, 12600, 1978, 15400, 12960

Offset

1,2

Links

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

Formula

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

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 3*p - 1)) = 1.256741057020447773244230946716370792268447699628630376844295183469512964116... - Vaclav Kotesovec, Sep 20 2020

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*n, {n, 1, 100}] (* G. C. Greubel, Jun 10 2016 *)

Crossrefs

Sequence in context: A241053 A068642 A198309 * A288781 A233451 A177172

Adjacent sequences: A167339 A167340 A167341 * A167343 A167344 A167345

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved