A167326 - OEIS

%I #11 Oct 21 2023 05:33:38

%S 1,35,42,1225,56,1470,70,42875,1764,1960,98,51450,112,2450,2352,

%T 1500625,140,61740,154,68600,2940,3430,182,1800750,3136,3920,74088,

%U 85750,224,82320,238,52521875,4116,4900,3920,2160900,280,5390,4704,2401000,308

%N Totally multiplicative sequence with a(p) = 7*(p+3) for prime p.

%H G. C. Greubel, <a href="/A167326/b167326.txt">Table of n, a(n) for n = 1..1000</a>

%F Multiplicative with a(p^e) = (7*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (7*(p(k)+3))^e(k).

%F a(n) = A165828(n) * A166591(n) = 7^bigomega(n) * A166591(n) = 7^A001222(n) * A166591(n).

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*7^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 09 2016 *)

%t f[p_, e_] := (7*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 21 2023 *)

%Y Cf. A001222, A165828, A166591.

%K nonn,easy,mult

%O 1,2

%A _Jaroslav Krizek_, Nov 01 2009