A138403 - OEIS

%I #21 Nov 22 2022 02:33:50

%S 8,54,500,2058,13310,26364,78608,123462,267674,682892,893730,1823508,

%T 2756840,3339294,4775858,7741604,11911982,13618860,19850358,25053770,

%U 28009224,38457042,46886534,62037272,87616608,103030100,111458154

%N a(n) = p^3*(p-1), where p = prime(n).

%H Vincenzo Librandi, <a href="/A138403/b138403.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Pri#prime_powers">Index to sequences related to prime powers</a>.

%F a(n) = A000010(prime(n)^4). - _R. J. Mathar_, Oct 15 2017

%F From _Amiram Eldar_, Nov 22 2022: (Start)

%F a(n) = prime(n)^4 - prime(n)^3 = A030514(n) - A030078(n).

%F Product_{n>=1} (1 - 1/a(n)) = A065415. (End)

%t a = {}; Do[p = Prime[n]; AppendTo[a, p^4 - p^3], {n, 1, 50}]; a

%o (PARI) forprime(p=2,1e3,print1(p^4-p^3", ")) \\ _Charles R Greathouse IV_, Jun 16 2011

%o (Magma) [NthPrime((n))^4 - NthPrime((n))^3: n in [1..40] ]; // _Vincenzo Librandi_, Jun 17 2011

%Y Cf. A000010, A030514, A030078, A065415.

%K nonn,easy

%O 1,1

%A _Artur Jasinski_, Mar 19 2008