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%I #31 May 16 2020 07:30:47
%S 1,4,45,80,28974,28974,8489103,80314575,5196065775,77506573550,
%T 166622964149389,489289301397948
%N Smallest initial number k of n consecutive numbers satisfying numdiv(k) > numdiv(k+1) > ... > numdiv(k+n-1).
%C a(11) > 10^12. - _Donovan Johnson_, Oct 13 2009
%C a(11) > 10^13. - _Giovanni Resta_, Jul 25 2013
%C a(13) > 2.64*10^15. - _Jud McCranie_, Mar 27 2019
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 45, p. 17, Ellipses, Paris 2008.
%e a(4) = 80, as tau(80) = 10 > tau(81) = 5 > tau(82) = 4 > tau(83) = 2.
%o (PARI) n=2; for(k=1, 100, while(1, m=n; s=1; while(numdiv(m)<numdiv(m-1), s=s+1; m=m+1); if(s>=k, print1(n-1, ", "); break); n=n+1))
%Y Cf. A075028, A075031.
%K nonn,more
%O 1,2
%A _Amarnath Murthy_, Sep 02 2002
%E Edited by _Ralf Stephan_, Mar 21 2003
%E Definition corrected by _Leroy Quet_, Feb 23 2008
%E 2 more terms from _Lekraj Beedassy_, Jul 13 2008
%E a(9)-a(10) from _Donovan Johnson_, Oct 13 2009
%E a(11)-a(12) from _Jud McCranie_, Mar 27 2019
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