A166650 - OEIS

%I #15 Feb 06 2025 08:22:19

%S 1,30,40,900,60,1200,80,27000,1600,1800,120,36000,140,2400,2400,

%T 810000,180,48000,200,54000,3200,3600,240,1080000,3600,4200,64000,

%U 72000,300,72000,320,24300000,4800,5400,4800,1440000,380,6000,5600,1620000,420

%N Totally multiplicative sequence with a(p) = 10*(p+1) for prime p.

%H G. C. Greubel, <a href="/A166650/b166650.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = (10*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (10*(p(k)+1))^e(k).

%F a(n) = A165831(n) * A003959(n) = 10^bigomega(n) * A003959(n) = 10^A001222(n) * A003959(n).

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*10^(PrimeOmega[n]), {n, 1, 100}](* _G. C. Greubel_, May 21 2016 *)

%t f[p_, e_] := (10*(p+1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 17 2023 *)

%Y Cf. A001222, A003959, A165831.

%K nonn,easy,mult

%O 1,2

%A _Jaroslav Krizek_, Oct 18 2009