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A167324
Totally multiplicative sequence with a(p) = 5*(p+3) for prime p.
1
1, 25, 30, 625, 40, 750, 50, 15625, 900, 1000, 70, 18750, 80, 1250, 1200, 390625, 100, 22500, 110, 25000, 1500, 1750, 130, 468750, 1600, 2000, 27000, 31250, 160, 30000, 170, 9765625, 2100, 2500, 2000, 562500, 200, 2750, 2400, 625000, 220, 37500, 230
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = (5*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)+3))^e(k).
a(n) = A165826(n) * A166591(n) = 5^bigomega(n) * A166591(n) = 5^A001222(n) * A166591(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*5^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (5*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 22 2023 *)
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved