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A135177 a(n) = p^2*(p-1), where p = prime(n).

%I A135177 #54 Dec 14 2024 17:46:22
%S A135177 4,18,100,294,1210,2028,4624,6498,11638,23548,28830,49284,67240,77658,
%T A135177 101614,146068,201898,223260,296274,352870,383688,486798,564898,
%U A135177 697048,903264,1020100,1082118,1213594,1283148,1430128,2032254,2230930
%N A135177 a(n) = p^2*(p-1), where p = prime(n).
%H A135177 Antti Karttunen, <a href="/A135177/b135177.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Vincenzo Librandi)
%H A135177 <a href="/index/Pri#prime_powers">Index to sequences related to prime powers</a>.
%F A135177 a(n) = p^3 - p^2 = A030078(n) - A001248(n).
%F A135177 a(n) = A000010(prime(n)^3). - _R. J. Mathar_, Oct 15 2017
%F A135177 Sum_{n>=1} 1/a(n) = A152441. - _Amiram Eldar_, Nov 09 2020
%F A135177 From _Amiram Eldar_, Nov 22 2022: (Start)
%F A135177 Product_{n>=1} (1 + 1/a(n)) = A065483.
%F A135177 Product_{n>=1} (1 - 1/a(n)) = A065414. (End)
%F A135177 a(n) = 2*A138416(n). - _Antti Karttunen_, Dec 14 2024
%e A135177 a(4) = 294 because the 4th prime number is 7, 7^2 = 49, 7-1 = 6 and 49 * 6 = 294.
%t A135177 Table[Prime[n]^3-Prime[n]^2, {n, 1, 12}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2008 *)
%t A135177 Table[p^3-p^2,{p,Prime[Range[40]]}] (* _Harvey P. Dale_, Jan 15 2015 *)
%o A135177 (Magma)[(p^3-p^2): p in PrimesUpTo(200)]; // _Vincenzo Librandi_, Dec 15 2010
%o A135177 (PARI) forprime(p=2,1e3,print1(p^2*(p-1)", ")) \\ _Charles R Greathouse IV_, Jun 16 2011
%o A135177 (PARI) A135177(n) = eulerphi(prime(n)^3); \\ _Antti Karttunen_, Dec 14 2024
%o A135177 (PARI) A135177(n) = ((p->(p-1)*p*p)(prime(n))); \\ _Antti Karttunen_, Dec 14 2024
%Y A135177 Cf. A001248 (p^2), A030078 (p^3), A045991 (n^2 * (n-1)), A065414, A065483, A138416 (terms halved), A152441.
%Y A135177 Column 4 of A379010.
%K A135177 nonn,easy
%O A135177 1,1
%A A135177 _Omar E. Pol_, Nov 25 2007