cp's OEIS Frontend

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.

%I A075046 #34 Aug 08 2023 22:47:56
%S A075046 1,1,1,1,241,241,12853,12853,234613,376741,78312721,125938261,
%T A075046 4019167441,16586155153,35237422882,1296230533473,42301168491121,
%U A075046 61118966262061
%N 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.
%C A075046 tau(k) <= tau(k+1) <= ... <= tau(k+n-1).
%C A075046 a(16) > 10^12. - _Donovan Johnson_, Oct 13 2009
%C A075046 a(17) > 10^13. - _Giovanni Resta_, Apr 12 2017
%C A075046 a(19) > 2.64*10^15. - _Jud McCranie_, Mar 27 2019
%C A075046 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
%e A075046 a(5) = 241 = a(6) as tau(241) = 2 < tau(242) = tau(243) = tau(244) = tau(245) = 6 < tau(246).
%t A075046 k = 1; Do[ While[t = Table[ DivisorSigma[0, i], {i, k, k + n - 1}]; t != Sort[t], k++ ]; Print[k], {n, 1, 11}]
%Y A075046 Cf. A075028, A075029, A075031, A045983, A006073, A075044, A055927, A075047.
%K A075046 nonn,more
%O A075046 1,5
%A A075046 _Amarnath Murthy_, Sep 03 2002
%E A075046 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003
%E A075046 a(11) from _Robert G. Wilson v_, Sep 07 2003
%E A075046 a(12)-a(15) from _Donovan Johnson_, Oct 13 2009
%E A075046 a(16) from _Fred Schneider_, Mar 29 2017
%E A075046 a(17)-a(18) from _Jud McCranie_, Mar 27 2019