A075046 a(n) = the smallest number k such that the number of divisors of the n numbers from k through k+n-1 are in nondescending order.

1, 1, 1, 1, 241, 241, 12853, 12853, 234613, 376741, 78312721, 125938261, 4019167441, 16586155153, 35237422882, 1296230533473, 42301168491121, 61118966262061

Offset: 1

Author

Amarnath Murthy, Sep 03 2002

Keywords

• nonn
• more

Comments

tau(k) <= tau(k+1) <= ... <= tau(k+n-1).

a(16) > 10^12. - Donovan Johnson, Oct 13 2009

a(17) > 10^13. - Giovanni Resta, Apr 12 2017

a(19) > 2.64*10^15. - Jud McCranie, Mar 27 2019

If a(n) > 1, then A013632(a(n)) >= n. Might be useful to help speed up brute force search. - Chai Wah Wu, May 04 2017

Examples

			a(5) = 241 = a(6) as tau(241) = 2 < tau(242) = tau(243) = tau(244) = tau(245) = 6 < tau(246).
		

Crossrefs

Cf. A075028, A075029, A075031, A045983, A006073, A075044, A055927, A075047.

Programs

Mathematica

k = 1; Do[ While[t = Table[ DivisorSigma[0, i], {i, k, k + n - 1}]; t != Sort[t], k++ ]; Print[k], {n, 1, 11}]

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003

a(11) from Robert G. Wilson v, Sep 07 2003

a(12)-a(15) from Donovan Johnson, Oct 13 2009

a(16) from Fred Schneider, Mar 29 2017

a(17)-a(18) from Jud McCranie, Mar 27 2019