A342930 Least positive number k such that n^n divides k*(k+1)/2.

1, 7, 26, 511, 3124, 16767, 823542, 33554431, 387420488, 1787109375, 285311670610, 6737830608896, 302875106592252, 10190301669556224, 12913848876953124, 36893488147419103231, 827240261886336764176, 22831345258932427292672, 1978419655660313589123978, 35357007743740081787109375

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..386 (terms < 10^1000)

Formula

a(p) = p^p - 1 for odd prime p. - David A. Corneth, Mar 29 2021

Example

  n |     a(n) |         T(a(n)) = n^n * A342931(n).
----+----------+------------------------------------
  1 |        1 |               1 = 1^1 * 1.
  2 |        7 |              28 = 2^2 * 7.
  3 |       26 |             351 = 3^3 * 13.
  4 |      511 |          130816 = 4^4 * 511.
  5 |     3124 |         4881250 = 5^5 * 1562.
  6 |    16767 |       140574528 = 6^6 * 3013.
  7 |   823542 |    339111124653 = 7^7 * 411771.
  8 | 33554431 | 562949936644096 = 8^8 * 33554431.

Prog

(PARI) a(n) = my(k=1, m=n^n); while(k*(k+1)/2%m!=0, k++); k;
(PARI) a(n) = { my(p = 2*n^n, f = factor(p), res = oo); for(i = 2^(#f~-1), 2^#f~-1, b = binary(i); pr = prod(j = 1, #f~, f[j, 1]^(b[j]*f[j, 2])); ipr = p/pr; for(j = -1, 0, c = lift(chinese(Mod(-1-j, ipr), Mod(j, pr))); if(c > 0, res = min(res, c)))); res } \\ David A. Corneth, Mar 29 2021

Crossrefs

Cf. A000217, A000312, A048861, A232097, A342931.

Sequence in context: A009375 A009380 A183329 * A166406 A243006 A175377

Adjacent sequences: A342927 A342928 A342929 * A342931 A342932 A342933

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 29 2021

Extensions

More terms from David A. Corneth, Mar 29 2021

Status

approved