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A095717 "Second order" highly composite numbers: the gap between the number of divisors (d(n)) rises to a new record. 1
2, 12, 120, 720, 2520, 5040, 110880, 1441440, 21621600, 367567200, 6983776800, 13967553600, 321253732800, 481880599200, 963761198400, 6746328388800, 55898149507200, 130429015516800, 195643523275200, 1732842634723200, 4043299481020800, 6064949221531200, 60649492215312000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A002182, A002183, A053640, A053624.

Sequence in context: A328857 A295864 A255506 * A089431 A119701 A286629

Adjacent sequences:  A095714 A095715 A095716 * A095718 A095719 A095720

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

Definition edited by Harvey P. Dale, Apr 09 2018

More terms from Amiram Eldar, Jul 17 2019

STATUS

approved

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Last modified September 25 02:25 EDT 2021. Contains 347651 sequences. (Running on oeis4.)