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A167330
Totally multiplicative sequence with a(p) = 2*(2p-1) = 4p-2 for prime p.
1
1, 6, 10, 36, 18, 60, 26, 216, 100, 108, 42, 360, 50, 156, 180, 1296, 66, 600, 74, 648, 260, 252, 90, 2160, 324, 300, 1000, 936, 114, 1080, 122, 7776, 420, 396, 468, 3600, 146, 444, 500, 3888, 162, 1560, 170, 1512, 1800, 540, 186, 12960, 676, 1944
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = (2*(2p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(2*p(k)-1))^e(k).
a(n) = A061142(n) * A166651(n) = 2^bigomega(n) * A166651(n) = 2^A001222(n) * A166651(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((2*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_] := (4*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] = 4*f[k, 1]-2; ); factorback(f); } \\ Michel Marcus, Jun 06 2016
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved