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

%I A342930 #25 Mar 30 2021 01:18:39
%S A342930 1,7,26,511,3124,16767,823542,33554431,387420488,1787109375,
%T A342930 285311670610,6737830608896,302875106592252,10190301669556224,
%U A342930 12913848876953124,36893488147419103231,827240261886336764176,22831345258932427292672,1978419655660313589123978,35357007743740081787109375
%N A342930 Least positive number k such that n^n divides k*(k+1)/2.
%H A342930 David A. Corneth, <a href="/A342930/b342930.txt">Table of n, a(n) for n = 1..386</a> (terms < 10^1000)
%F A342930 a(p) = p^p - 1 for odd prime p. - _David A. Corneth_, Mar 29 2021
%e A342930   n |     a(n) |         T(a(n)) = n^n * A342931(n).
%e A342930 ----+----------+------------------------------------
%e A342930   1 |        1 |               1 = 1^1 * 1.
%e A342930   2 |        7 |              28 = 2^2 * 7.
%e A342930   3 |       26 |             351 = 3^3 * 13.
%e A342930   4 |      511 |          130816 = 4^4 * 511.
%e A342930   5 |     3124 |         4881250 = 5^5 * 1562.
%e A342930   6 |    16767 |       140574528 = 6^6 * 3013.
%e A342930   7 |   823542 |    339111124653 = 7^7 * 411771.
%e A342930   8 | 33554431 | 562949936644096 = 8^8 * 33554431.
%o A342930 (PARI) a(n) = my(k=1, m=n^n); while(k*(k+1)/2%m!=0, k++); k;
%o A342930 (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
%Y A342930 Cf. A000217, A000312, A048861, A232097, A342931.
%K A342930 nonn,easy
%O A342930 1,2
%A A342930 _Seiichi Manyama_, Mar 29 2021
%E A342930 More terms from _David A. Corneth_, Mar 29 2021