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a(n) = (p^3 - p^2)/2, where p = prime(n).
3

%I #16 Sep 08 2022 08:45:33

%S 2,9,50,147,605,1014,2312,3249,5819,11774,14415,24642,33620,38829,

%T 50807,73034,100949,111630,148137,176435,191844,243399,282449,348524,

%U 451632,510050,541059,606797,641574,715064,1016127,1115465,1276292,1333149

%N a(n) = (p^3 - p^2)/2, where p = prime(n).

%C Differences (p^k - p^m)/q with k > m:

%C .

%C expression OEIS sequence

%C -------------- -------------

%C p^2 - p A036689

%C (p^2 - p)/2 A008837

%C p^3 - p A127917

%C (p^3 - p)/2 A127918

%C (p^3 - p)/3 A127919

%C (p^3 - p)/6 A127920

%C p^3 - p^2 A135177

%C (p^3 - p^2)/2 this sequence

%C p^4 - p A138401

%C (p^4 - p)/2 A138417

%C p^4 - p^2 A138402

%C (p^4 - p^2)/2 A138418

%C (p^4 - p^2)/3 A138419

%C (p^4 - p^2)/4 A138420

%C (p^4 - p^2)/6 A138421

%C (p^4 - p^2)/12 A138422

%C p^4 - p^3 A138403

%C (p^4 - p^3)/2 A138423

%C p^5 - p A138404

%C (p^5 - p)/2 A138424

%C (p^5 - p)/3 A138425

%C (p^5 - p)/5 A138426

%C (p^5 - p)/6 A138427

%C (p^5 - p)/10 A138428

%C (p^5 - p)/15 A138429

%C (p^5 - p)/30 A138430

%C p^5 - p^2 A138405

%C (p^5 - p^2)/2 A138431

%C p^5 - p^3 A138406

%C (p^5 - p^3)/2 A138432

%C (p^5 - p^3)/3 A138433

%C (p^5 - p^3)/4 A138434

%C (p^5 - p^3)/6 A138435

%C (p^5 - p^3)/8 A138436

%C (p^5 - p^3)/12 A138437

%C (p^5 - p^3)/24 A138438

%C p^5 - p^4 A138407

%C (p^5 - p^4)/2 A138439

%C p^6 - p A138408

%C (p^6 - p)/2 A138440

%C p^6 - p^2 A138409

%C (p^6 - p^2)/2 A138441

%C (p^6 - p^2)/3 A138442

%C (p^6 - p^2)/4 A138443

%C (p^6 - p^2)/5 A138444

%C (p^6 - p^2)/6 A138445

%C (p^6 - p^2)/10 A138446

%C (p^6 - p^2)/12 A138447

%C (p^6 - p^2)/15 A138448

%C (p^6 - p^2)/20 A122220

%C (p^6 - p^2)/30 A138450

%C (p^6 - p^2)/60 A138451

%C p^6 - p^3 A138410

%C (p^6 - p^3)/2 A138452

%C p^6 - p^4 A138411

%C (p^6 - p^4)/2 A138453

%C (p^6 - p^4)/3 A138454

%C (p^6 - p^4)/4 A138455

%C (p^6 - p^4)/6 A138456

%C (p^6 - p^4)/8 A138457

%C (p^6 - p^4)/12 A138458

%C (p^6 - p^4)/24 A138459

%C p^6 - p^5 A138412

%C (p^6 - p^5)/2 A138460

%H Vincenzo Librandi, <a href="/A138416/b138416.txt">Table of n, a(n) for n = 1..168</a>

%t a = {}; Do[p = Prime[n]; AppendTo[a, (p^3 - p^2)/2], {n, 1, 50}]; a

%t (#^3-#^2)/2&/@Prime[Range[50]] (* _Harvey P. Dale_, Nov 01 2020 *)

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

%o (Magma)[(p^3-p^2)/2: p in PrimesUpTo(1000)]; // _Vincenzo Librandi_, Jun 17 2011

%K nonn,easy

%O 1,1

%A _Artur Jasinski_, Mar 19 2008

%E Definition corrected by _T. D. Noe_, Aug 25 2008