This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A138416 #21 Dec 12 2024 23:33:31
%S A138416 2,9,50,147,605,1014,2312,3249,5819,11774,14415,24642,33620,38829,
%T A138416 50807,73034,100949,111630,148137,176435,191844,243399,282449,348524,
%U A138416 451632,510050,541059,606797,641574,715064,1016127,1115465,1276292,1333149
%N A138416 a(n) = (p^3 - p^2)/2, where p = prime(n).
%C A138416 Differences (p^k - p^m)/q with k > m:
%C A138416 expression OEIS sequence
%C A138416 -------------- -------------
%C A138416 p^2 - p A036689
%C A138416 (p^2 - p)/2 A008837
%C A138416 p^3 - p A127917
%C A138416 (p^3 - p)/2 A127918
%C A138416 (p^3 - p)/3 A127919
%C A138416 (p^3 - p)/6 A127920
%C A138416 p^3 - p^2 A135177
%C A138416 (p^3 - p^2)/2 this sequence
%C A138416 p^4 - p A138401
%C A138416 (p^4 - p)/2 A138417
%C A138416 p^4 - p^2 A138402
%C A138416 (p^4 - p^2)/2 A138418
%C A138416 (p^4 - p^2)/3 A138419
%C A138416 (p^4 - p^2)/4 A138420
%C A138416 (p^4 - p^2)/6 A138421
%C A138416 (p^4 - p^2)/12 A138422
%C A138416 p^4 - p^3 A138403
%C A138416 (p^4 - p^3)/2 A138423
%C A138416 p^5 - p A138404
%C A138416 (p^5 - p)/2 A138424
%C A138416 (p^5 - p)/3 A138425
%C A138416 (p^5 - p)/5 A138426
%C A138416 (p^5 - p)/6 A138427
%C A138416 (p^5 - p)/10 A138428
%C A138416 (p^5 - p)/15 A138429
%C A138416 (p^5 - p)/30 A138430
%C A138416 p^5 - p^2 A138405
%C A138416 (p^5 - p^2)/2 A138431
%C A138416 p^5 - p^3 A138406
%C A138416 (p^5 - p^3)/2 A138432
%C A138416 (p^5 - p^3)/3 A138433
%C A138416 (p^5 - p^3)/4 A138434
%C A138416 (p^5 - p^3)/6 A138435
%C A138416 (p^5 - p^3)/8 A138436
%C A138416 (p^5 - p^3)/12 A138437
%C A138416 (p^5 - p^3)/24 A138438
%C A138416 p^5 - p^4 A138407
%C A138416 (p^5 - p^4)/2 A138439
%C A138416 p^6 - p A138408
%C A138416 (p^6 - p)/2 A138440
%C A138416 p^6 - p^2 A138409
%C A138416 (p^6 - p^2)/2 A138441
%C A138416 (p^6 - p^2)/3 A138442
%C A138416 (p^6 - p^2)/4 A138443
%C A138416 (p^6 - p^2)/5 A138444
%C A138416 (p^6 - p^2)/6 A138445
%C A138416 (p^6 - p^2)/10 A138446
%C A138416 (p^6 - p^2)/12 A138447
%C A138416 (p^6 - p^2)/15 A138448
%C A138416 (p^6 - p^2)/20 A122220
%C A138416 (p^6 - p^2)/30 A138450
%C A138416 (p^6 - p^2)/60 A138451
%C A138416 p^6 - p^3 A138410
%C A138416 (p^6 - p^3)/2 A138452
%C A138416 p^6 - p^4 A138411
%C A138416 (p^6 - p^4)/2 A138453
%C A138416 (p^6 - p^4)/3 A138454
%C A138416 (p^6 - p^4)/4 A138455
%C A138416 (p^6 - p^4)/6 A138456
%C A138416 (p^6 - p^4)/8 A138457
%C A138416 (p^6 - p^4)/12 A138458
%C A138416 (p^6 - p^4)/24 A138459
%C A138416 p^6 - p^5 A138412
%C A138416 (p^6 - p^5)/2 A138460
%C A138416 .
%C A138416 We can prove that for n>1, a(n) is the remainder of the Euclidean division of Sum_{k=0..p-1} k^p by p^3 where p = prime(n). - _Pierre Vandaële_, Nov 30 2024
%H A138416 Vincenzo Librandi, <a href="/A138416/b138416.txt">Table of n, a(n) for n = 1..168</a>
%t A138416 a = {}; Do[p = Prime[n]; AppendTo[a, (p^3 - p^2)/2], {n, 1, 50}]; a
%t A138416 (#^3-#^2)/2&/@Prime[Range[50]] (* _Harvey P. Dale_, Nov 01 2020 *)
%o A138416 (PARI) forprime(p=2,1e3,print1((p^3-p^2)/2", ")) \\ _Charles R Greathouse IV_, Jun 16 2011
%o A138416 (Magma)[(p^3-p^2)/2: p in PrimesUpTo(1000)]; // _Vincenzo Librandi_, Jun 17 2011
%K A138416 nonn,easy
%O A138416 1,1
%A A138416 _Artur Jasinski_, Mar 19 2008
%E A138416 Definition corrected by _T. D. Noe_, Aug 25 2008