A166649 Totally multiplicative sequence with a(p) = 9*(p+1) for prime p.

1, 27, 36, 729, 54, 972, 72, 19683, 1296, 1458, 108, 26244, 126, 1944, 1944, 531441, 162, 34992, 180, 39366, 2592, 2916, 216, 708588, 2916, 3402, 46656, 52488, 270, 52488, 288, 14348907, 3888, 4374, 3888, 944784, 342, 4860, 4536, 1062882, 378

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (9*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)+1))^e(k).

a(n) = A165830(n) * A003959(n) = 9^bigomega(n) * A003959(n) = 9^A001222(n) * A003959(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*9^(PrimeOmega[n]), {n, 1, 100}] (* G. C. Greubel, May 21 2016 *)
f[p_, e_] := (9*(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] = 9*(f[k, 1]+1)); factorback(f); } \\ Michel Marcus, May 21 2016

Crossrefs

Cf. A001222, A003959, A165830.

Sequence in context: A160379 A351473 A152053 * A025145 A266963 A180961

Adjacent sequences: A166646 A166647 A166648 * A166650 A166651 A166652

Keyword

nonn,easy,mult,changed

Author

Jaroslav Krizek, Oct 18 2009

Status

approved