A166650 Totally multiplicative sequence with a(p) = 10*(p+1) for prime p.

1, 30, 40, 900, 60, 1200, 80, 27000, 1600, 1800, 120, 36000, 140, 2400, 2400, 810000, 180, 48000, 200, 54000, 3200, 3600, 240, 1080000, 3600, 4200, 64000, 72000, 300, 72000, 320, 24300000, 4800, 5400, 4800, 1440000, 380, 6000, 5600, 1620000, 420

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = (10*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (10*(p(k)+1))^e(k).

a(n) = A165831(n) * A003959(n) = 10^bigomega(n) * A003959(n) = 10^A001222(n) * A003959(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*10^(PrimeOmega[n]), {n, 1, 100}](* G. C. Greubel, May 21 2016 *)
f[p_, e_] := (10*(p+1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 17 2023 *)

Crossrefs

Cf. A001222, A003959, A165831.

Sequence in context: A309306 A103250 A181638 * A275193 A225049 A043120

Adjacent sequences: A166647 A166648 A166649 * A166651 A166652 A166653

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved