A166644 Totally multiplicative sequence with a(p) = 4*(p+1) for prime p.

1, 12, 16, 144, 24, 192, 32, 1728, 256, 288, 48, 2304, 56, 384, 384, 20736, 72, 3072, 80, 3456, 512, 576, 96, 27648, 576, 672, 4096, 4608, 120, 4608, 128, 248832, 768, 864, 768, 36864, 152, 960, 896, 41472, 168, 6144, 176, 6912, 6144, 1152, 192, 331776

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (4*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)+1)^e(k).

a(n) = A165825(n) * A003959(n) = 4^bigomega(n) * A003959(n) = 4^A001222(n) * A003959(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*4^(PrimeOmega[n]), {n, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (4*(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] = 4*(f[k, 1]+1)); factorback(f); } \\ Michel Marcus, May 21 2016

Crossrefs

Cf. A001222, A003959, A165825.

Sequence in context: A377906 A050555 A060669 * A264492 A264485 A278034

Adjacent sequences: A166641 A166642 A166643 * A166645 A166646 A166647

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved