A075029 Smallest initial number k of n consecutive numbers satisfying numdiv(k) > numdiv(k+1) > ... > numdiv(k+n-1).

1, 4, 45, 80, 28974, 28974, 8489103, 80314575, 5196065775, 77506573550, 166622964149389, 489289301397948

Offset

1,2

Comments

a(11) > 10^12. - Donovan Johnson, Oct 13 2009

a(11) > 10^13. - Giovanni Resta, Jul 25 2013

a(13) > 2.64*10^15. - Jud McCranie, Mar 27 2019

References

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 45, p. 17, Ellipses, Paris 2008.

Links

Table of n, a(n) for n=1..12.

Example

a(4) = 80, as tau(80) = 10 > tau(81) = 5 > tau(82) = 4 > tau(83) = 2.

Prog

(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))

Crossrefs

Cf. A075028, A075031.

Sequence in context: A024254 A167781 A173327 * A369228 A070225 A132998

Adjacent sequences: A075026 A075027 A075028 * A075030 A075031 A075032

Keyword

nonn,more

Author

Amarnath Murthy, Sep 02 2002

Extensions

Edited by Ralf Stephan, Mar 21 2003

Definition corrected by Leroy Quet, Feb 23 2008

2 more terms from Lekraj Beedassy, Jul 13 2008

a(9)-a(10) from Donovan Johnson, Oct 13 2009

a(11)-a(12) from Jud McCranie, Mar 27 2019

Status

approved