A166647 - OEIS

%I #14 Oct 18 2023 02:09:43

%S 1,21,28,441,42,588,56,9261,784,882,84,12348,98,1176,1176,194481,126,

%T 16464,140,18522,1568,1764,168,259308,1764,2058,21952,24696,210,24696,

%U 224,4084101,2352,2646,2352,345744,266,2940,2744,388962,294,32928,308

%N Totally multiplicative sequence with a(p) = 7*(p+1) for prime p.

%H G. C. Greubel, <a href="/A166647/b166647.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = (7*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (7*(p(k)+1)^e(k).

%F a(n) = A165828(n) * A003959(n) = 7^bigomega(n) * A003959(n) = 7^A001222(n) * A003959(n).

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*7^(PrimeOmega[n]), {n, 1, 100}] (* _G. C. Greubel_, May 20 2016 *)

%t f[p_, e_] := (7*(p+1))^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] = 7*(f[k,1]+1)); factorback(f);} \\ _Michel Marcus_, May 21 2016

%Y Cf. A001222, A003959, A165828.

%K nonn,easy,mult

%O 1,2

%A _Jaroslav Krizek_, Oct 18 2009