

A123000


a(n) is the smallest positive integer such that d(a(n))*d(a(n)+1) > d(a(n1))*d(a(n1)+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
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OFFSET

1,2


COMMENTS

a(n) also equals the smallest positive integer such that d(a(n)(a(n)+1)) > d(a(n1)(a(n1)+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

Table of n, a(n) for n=1..41.


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



