A095717 "Second order" highly composite numbers: the gap between the number of divisors (d(n)) rises to a new record.

2, 12, 120, 720, 2520, 5040, 110880, 1441440, 21621600, 367567200, 6983776800, 13967553600, 321253732800, 481880599200, 963761198400, 6746328388800, 55898149507200, 130429015516800, 195643523275200, 1732842634723200, 4043299481020800, 6064949221531200, 60649492215312000

Offset: 1

Author

Stefano Lanfranco (lastefano(AT)yahoo.it), Jul 08 2004

Keywords

• easy
• nonn

Comments

The corresponding indices of the highly composite numbers are 2, 5, 10, 14, 18, 19, 30, 40, ... (see the link for more values). - Amiram Eldar, Jul 17 2019

Examples

			120 is in the sequence because d(120)=16 and the previous highly composite number is 60 with d(60)=12, the gap between the number of divisor 16-12=4 is the maximum with number <=120
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1374
• Amiram Eldar, Table of n and k such that A002182(k) = a(n) for n = 1..1374

Crossrefs

Cf. A002182, A002183, A053640, A053624.

Programs

Mathematica

s={}; dmax = dmprev= gapmax=0; Do[d = DivisorSigma[0, k]; If[d > dmax ,  dmprev = dmax; dmax = d; gap = dmax - dmprev ;If[gap > gapmax, gapmax = gap; AppendTo[s, k]]], {k, 1, 1500000}]; s (* Amiram Eldar, Jul 17 2019 *)

Extensions

Definition edited by Harvey P. Dale, Apr 09 2018

More terms from Amiram Eldar, Jul 17 2019