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, 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

Offset: 1

Author

Leroy Quet, Jul 06 2008

Keywords

• nonn

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

Examples

			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.
		

Crossrefs

Cf. A002378 (oblong numbers), A092517.

Programs

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

Extensions

More terms from Max Alekseyev, Apr 26 2010