A166645 Totally multiplicative sequence with a(p) = 5*(p+1) for prime p.

1, 15, 20, 225, 30, 300, 40, 3375, 400, 450, 60, 4500, 70, 600, 600, 50625, 90, 6000, 100, 6750, 800, 900, 120, 67500, 900, 1050, 8000, 9000, 150, 9000, 160, 759375, 1200, 1350, 1200, 90000, 190, 1500, 1400, 101250, 210, 12000, 220, 13500, 12000, 1800

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (5*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)+1)^e(k).

a(n) = A165826(n) * A003959(n) = 5^bigomega(n) * A003959(n) = 5^A001222(n) * A003959(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*5^(PrimeOmega[n]), {n, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (5*(p+1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 17 2023 *)

Prog

(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = 5*(f[k, 1]+1)); factorback(f); } \\ Michel Marcus, May 21 2016

Crossrefs

Cf. A001222, A003959, A165826.

Sequence in context: A043125 A043905 A072310 * A033708 A343821 A294171

Adjacent sequences: A166642 A166643 A166644 * A166646 A166647 A166648

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved