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A323278 Numbers of the form p^2-1 that have a record-breaking number of divisors, where p is prime. 1
3, 8, 24, 48, 120, 288, 360, 840, 1680, 5040, 11880, 32760, 143640, 201600, 491400, 776160, 2042040, 3500640, 7447440, 9480240, 17297280, 34234200, 143256960, 514337040, 555120720, 569729160, 1656408600, 4283571600, 8148853440, 10951831800, 35415099720, 51437786400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(11)-a(26) from Chuck Gaydos.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..63

Chris Caldwell and G. L. Honaker, Jr., Prime Curio for 23869

EXAMPLE

a(7) = 360 because 360 has a record-breaking 24 divisors and 360 = p^2-1, where p = 19 is prime.

MATHEMATICA

Block[{s = Prime[Range[10^5]]^2 - 1, t}, t = DivisorSigma[0, s]; Map[s[[FirstPosition[t, #][[1]] ]] &, Union@ FoldList[Max, t]]] (* Michael De Vlieger, Jan 19 2019 *)

PROG

(PARI) lista(nn) = {my(m = 0, p = 2, np); for (n=1, nn, np = p^2-1; if (((nd = numdiv(np)) > m), print1(np, ", "); m = nd); p = nextprime(p+1); ); } \\ Michel Marcus, Jan 12 2019

(Python)

from sympy import divisor_count, nextprime

A323278_list, p, nmax = [], 2 , -1

while len(A323278_list) < 100:

    n = divisor_count(p**2-1)

    if n > nmax:

        nmax = n

        A323278_list.append(p**2-1)

    p = nextprime(p) # Chai Wah Wu, Feb 09 2019

CROSSREFS

Cf. A000005, A084920.

Sequence in context: A037450 A081990 A084920 * A026556 A096001 A080097

Adjacent sequences:  A323275 A323276 A323277 * A323279 A323280 A323281

KEYWORD

nonn

AUTHOR

G. L. Honaker, Jr., Jan 11 2019

EXTENSIONS

a(27)-a(32) from Daniel Suteu, Jan 12 2019

STATUS

approved

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Last modified September 22 07:34 EDT 2020. Contains 337289 sequences. (Running on oeis4.)