|
%I #13 Oct 18 2023 02:10:14
%S 1,18,28,324,48,504,68,5832,784,864,108,9072,128,1224,1344,104976,168,
%T 14112,188,15552,1904,1944,228,163296,2304,2304,21952,22032,288,24192,
%U 308,1889568,3024,3024,3264,254016,368,3384,3584,279936,408,34272,428
%N Totally multiplicative sequence with a(p) = 2*(5p-1) = 10p-2 for prime p.
%H G. C. Greubel, <a href="/A167333/b167333.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = (2*(5p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(5*p(k)-1))^e(k).
%F a(n) = A061142(n) * A166654(n) = 2^bigomega(n) * A166654(n) = 2^A001222(n) * A166654(n).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((5*fi[[All, 1]] - 1)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 06 2016 *)
%t f[p_, e_] := (10*p-2)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 18 2023 *)
%o (PARI) a(n) = {my(f=factor(n)); for (k=1, #f~, f[k,1] = 10*f[k,1]-2;); factorback(f);} \\ _Michel Marcus_, Jun 06 2016
%Y Cf. A001222, A061142, A166654.
%K nonn,easy,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009
|
