The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A123000 a(n) is the smallest positive integer such that d(a(n))*d(a(n)+1) > d(a(n-1))*d(a(n-1)+1), where d(m) is the number of divisors of m and n > 1; a(1) = 1. 1
 1, 2, 3, 5, 8, 14, 15, 20, 35, 63, 80, 99, 104, 195, 224, 384, 440, 560, 935, 1224, 1539, 2015, 2079, 5264, 5984, 12375, 21735, 41040, 78624, 123200, 126224, 156519, 176175, 201824, 313599, 338624, 395199, 453375, 638000, 1154439, 1890944 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) also equals the smallest positive integer such that d(a(n)(a(n)+1)) > d(a(n-1)(a(n-1)+1)). That is, this is the sequence of indices of oblong numbers that have more divisors than the preceding oblong numbers. - Michel Marcus, Jul 13 2019 LINKS EXAMPLE Since a(7) = 15, we want for a(8) the smallest positive integer m such that d(m)*d(m+1) > d(15)d(16) = 4*5=20. Checking: d(16)*d(17)=10, d(17)*d(18)=12, d(18)*d(19)=12, d(19)*d(20)=12. All of these are <= 20. But d(20)*d(21) = 6*4=24, which is > 20. So a(8) = 20. PROG (PARI) lista(nn) = {my(m = 0, nm); for (n=1, nn, if ((nm = numdiv(n*(n+1))) > m, m = nm; print1(n, ", ")); ); } \\ Michel Marcus, Jul 13 2019 CROSSREFS Cf. A002378 (oblong numbers), A092517. Sequence in context: A041101 A041809 A117566 * A132599 A082931 A034413 Adjacent sequences:  A122997 A122998 A122999 * A123001 A123002 A123003 KEYWORD nonn AUTHOR Leroy Quet, Jul 06 2008 EXTENSIONS More terms from Max Alekseyev, Apr 26 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 28 05:17 EST 2020. Contains 338699 sequences. (Running on oeis4.)