cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A073826 Primes of the form Sum_{k=1..n} k^k, i.e., primes in A001923.

Original entry on oeis.org

5, 3413, 50069, 10405071317, 208492413443704093346554910065262730566475781
Offset: 1

Views

Author

Rick L. Shepherd, Aug 13 2002

Keywords

Comments

a(3) = A001923(10) = 10405071317 and the 45-digit a(4) = A001923(30) have been certified prime with Primo. Any additional terms are too big to include here.
The next term would have over 20000 digits; see A073825 for more information and updates.

Examples

			a(1) = 5 = 1^1 + 2^2 is the smallest prime of the form A001923(n) = sum_{k=1..n} k^k, namely for n = 2 = A073825(1).
a(2) = sum_{k=1..A073825(2)} k^k = 1^1 + 2^2 + 3^3 + 4^4 + 5^5 = 3413, a prime, so 3413 is in this sequence (A073825(2) = 5).

Crossrefs

Cf. A073825 (corresponding n), A001923 (sum_{k=1..n} k^k).
Cf. A122166 (indices of primes in A062970 (sum_{k=0..n} k^k)).

Programs

  • Mathematica
    Select[s=0;Table[s+=n^n,{n,5!}],PrimeQ[ # ]&] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)
  • PARI
    s=0; for(k=1,1320, s=s+k^k; if(isprime(s), print1(s,",")))

Formula

a(j) = A001923(A073825(j)) = sum_{k=1..A073825(j)} k^k.
Intersection of A001923 with A000040.

Extensions

Edited by M. F. Hasler, Mar 22 2008
Typo in comment corrected by Jonathan Vos Post, Mar 23 2008

A175232 The smallest prime divisor of 1 + 2^2 + 3^3 + ... + n^n.

Original entry on oeis.org

5, 2, 2, 3413, 50069, 2, 2, 7, 10405071317, 2, 2, 88799, 3, 2, 2, 3, 3, 2, 2, 5, 3, 2, 2, 3, 7, 2, 2, 7, 208492413443704093346554910065262730566475781, 2, 2, 3, 17, 2, 2, 5, 61, 2, 2, 71, 11, 2, 2, 11, 7, 2, 2, 5, 3, 2, 2, 3, 3, 2, 2, 23, 3, 2, 2, 3, 44818693, 2, 2, 5
Offset: 2

Views

Author

Michel Lagneau, Mar 09 2010

Keywords

Examples

			a(2) = 5 divides 1 + 2^2.
a(3) = 2 divides 1 + 2^2 + 3^3 = 32.
a(4) = 2 divides 1 + 2^2 + 3^3 + 4^4 = 288.
a(5) = 3413 divides 1 + 2^2 + 3^3 + 4^4 + 5^5 = 3413.
a(13) = 88799 divides 1 + 2^2 + 3^3 + ... + 13^13 = 88799 * 3514531963.

Crossrefs

Cf. A073826, A122166.

Programs

  • Maple
    with(numtheory): s :=1: for n from 2 to 60 do ;s := s+ n^n: s1 := ifactors(s)[2] : s2 :=s1[i][1], i=1..nops(s1):print(s1[1][1]):od:
  • Mathematica
    a[n_] := FactorInteger[Sum[k^k, {k, 1, n}]][[1, 1]]; Array[a, 20, 2] (* Amiram Eldar, Feb 04 2020 *)

Formula

a(n) = A020639(A001923(n)).

Extensions

Edited by R. J. Mathar, Mar 16 2010
a(61)-a(65) from Amiram Eldar, Feb 04 2020

A214662 Greatest prime divisor of 1 + 2^2 + 3^3 + ... + n^n.

Original entry on oeis.org

5, 2, 3, 3413, 50069, 8089, 487, 2099, 10405071317, 1274641129, 164496735539, 3514531963, 15624709, 23747111, 10343539, 56429700667, 1931869473647715169, 2383792821710269, 144326697012150473, 2053857208873393249, 128801386946535261205906957, 2298815880166789
Offset: 2

Views

Author

Michel Lagneau, Jul 24 2012

Keywords

Examples

			a(2) = 5 divides 1 + 2^2 ;
a(3) = 2 divides 1 + 2^2 + 3^3 = 32 ;
a(4) = 3 divides 1 + 2^2 + 3^3 + 4^4 = 288 = 2^5*3^2 ;
a(5) = 3413 divides 1 + 2^2 + 3^3 + 4^4 + 5^5 = 3413.
a(13) = 3514531963 divides 1 + 2^2 + 3^3 + ... + 13^13 = 88799 * 3514531963.

Links

Crossrefs

Cf. A001923, A006530, A073826, A122166, A175232.

Programs

  • Magma
    [Max(PrimeDivisors(&+[k^k:k in [1..n]])):n in [2..23]]; // Marius A. Burtea, Feb 09 2020
  • Maple
    with (numtheory):
s:= proc(n) option remember; `if`(n=1, 1, s(n-1)+n^n) end:
a:= n-> max(factorset(s(n))[]):
seq (a(n), n=2..23);  # Alois P. Heinz, Jul 24 2012
  • Mathematica
    s = 1; Table[s = s + n^n; FactorInteger[s][[-1, 1]], {n, 2, 24}] (* T. D. Noe, Jul 25 2012 *)
Module[{nn=30,lst},lst=Table[n^n,{n,nn}];Table[FactorInteger[Total[Take[lst,k]]][[-1,1]],{k,2,nn}]] (* Harvey P. Dale, Oct 09 2022 *)
  • PARI
    a(n) = vecmax(factor(sum(k=1, n, k^k))[,1]); \\ Michel Marcus, Feb 09 2020

Formula

a(n) = A006530(A001923(n)).
Showing 1-3 of 3 results.

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