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A167332
Totally multiplicative sequence with a(p) = 2*(4p-1) = 8p-2 for prime p.
1
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
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = (2*(4p-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).
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved