A166647 Totally multiplicative sequence with a(p) = 7*(p+1) for prime p.

1, 21, 28, 441, 42, 588, 56, 9261, 784, 882, 84, 12348, 98, 1176, 1176, 194481, 126, 16464, 140, 18522, 1568, 1764, 168, 259308, 1764, 2058, 21952, 24696, 210, 24696, 224, 4084101, 2352, 2646, 2352, 345744, 266, 2940, 2744, 388962, 294, 32928, 308

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (7*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (7*(p(k)+1)^e(k).

a(n) = A165828(n) * A003959(n) = 7^bigomega(n) * A003959(n) = 7^A001222(n) * A003959(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*7^(PrimeOmega[n]), {n, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (7*(p+1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 18 2023 *)

Prog

(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = 7*(f[k, 1]+1)); factorback(f); } \\ Michel Marcus, May 21 2016

Crossrefs

Cf. A001222, A003959, A165828.

Sequence in context: A048067 A344603 A212192 * A119107 A004196 A211253

Adjacent sequences: A166644 A166645 A166646 * A166648 A166649 A166650

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved