A167332 Totally multiplicative sequence with a(p) = 2*(4*p-1) = 8*p-2 for prime p.

1, 14, 22, 196, 38, 308, 54, 2744, 484, 532, 86, 4312, 102, 756, 836, 38416, 134, 6776, 150, 7448, 1188, 1204, 182, 60368, 1444, 1428, 10648, 10584, 230, 11704, 246, 537824, 1892, 1876, 2052, 94864, 294, 2100, 2244, 104272, 326, 16632, 342, 16856

Offset: 1

Author

Jaroslav Krizek, Nov 01 2009

Keywords

• nonn
• easy
• mult

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001222, A061142, A166653.

Programs

Maple

f:=n -> mul((8*t[1]-2)^t[2],t=ifactors(n)[2]):
map(f, [$1..100]); # Robert Israel, Jun 06 2016

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((4*fi[[All, 1]] - 1)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 06 2016 *)
f[p_, e_] := (8*p-2)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 18 2023 *)

PARI

a(n) = {my(f=factor(n)); for (k=1, #f~, f[k,1] = 8*f[k,1]-2;); factorback(f);} \\ Michel Marcus, Jun 06 2016

Formula

Multiplicative with a(p^e) = (2*(4*p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(4*p(k)-1))^e(k).

a(n) = A061142(n) * A166653(n) = 2^bigomega(n) * A166653(n) = 2^A001222(n) * A166653(n).