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A166642
Totally multiplicative sequence with a(p) = 2*(p+1) for prime p.
2
1, 6, 8, 36, 12, 48, 16, 216, 64, 72, 24, 288, 28, 96, 96, 1296, 36, 384, 40, 432, 128, 144, 48, 1728, 144, 168, 512, 576, 60, 576, 64, 7776, 192, 216, 192, 2304, 76, 240, 224, 2592, 84, 768, 88, 864, 768, 288, 96, 10368, 256, 864
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = (2*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(p(k)+1)^e(k).
a(n) = A061142(n) * A003959(n) = 2^bigomega(n) * A003959(n) = 2^A001222(n) * A003959(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*2^(PrimeOmega[n]), {n, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (2*(p+1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 18 2023 *)
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Jaroslav Krizek, Oct 18 2009
STATUS
approved