A138416 a(n) = (p^3 - p^2)/2, where p = prime(n).

2, 9, 50, 147, 605, 1014, 2312, 3249, 5819, 11774, 14415, 24642, 33620, 38829, 50807, 73034, 100949, 111630, 148137, 176435, 191844, 243399, 282449, 348524, 451632, 510050, 541059, 606797, 641574, 715064, 1016127, 1115465, 1276292, 1333149

Offset: 1

Author

Artur Jasinski, Mar 19 2008

Keywords

• nonn
• easy

Comments

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

expression OEIS sequence

-------------- -------------

p^2 - p A036689

(p^2 - p)/2 A008837

p^3 - p A127917

(p^3 - p)/2 A127918

(p^3 - p)/3 A127919

(p^3 - p)/6 A127920

p^3 - p^2 A135177

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

p^4 - p A138401

(p^4 - p)/2 A138417

p^4 - p^2 A138402

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

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

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

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

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

p^4 - p^3 A138403

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

p^5 - p A138404

(p^5 - p)/2 A138424

(p^5 - p)/3 A138425

(p^5 - p)/5 A138426

(p^5 - p)/6 A138427

(p^5 - p)/10 A138428

(p^5 - p)/15 A138429

(p^5 - p)/30 A138430

p^5 - p^2 A138405

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

p^5 - p^3 A138406

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

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

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

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

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

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

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

p^5 - p^4 A138407

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

p^6 - p A138408

(p^6 - p)/2 A138440

p^6 - p^2 A138409

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

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

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

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

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

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

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

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

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

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

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

p^6 - p^3 A138410

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

p^6 - p^4 A138411

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

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

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

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

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

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

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

p^6 - p^5 A138412

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

.

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..168

Programs

Magma

[(p^3-p^2)/2: p in PrimesUpTo(1000)]; // Vincenzo Librandi, Jun 17 2011

Mathematica

a = {}; Do[p = Prime[n]; AppendTo[a, (p^3 - p^2)/2], {n, 1, 50}]; a
(#^3-#^2)/2&/@Prime[Range[50]] (* Harvey P. Dale, Nov 01 2020 *)

PARI

forprime(p=2,1e3,print1((p^3-p^2)/2", ")) \\ Charles R Greathouse IV, Jun 16 2011

Extensions

Definition corrected by T. D. Noe, Aug 25 2008