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A323278
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Numbers of the form p^2-1 that have a record-breaking number of divisors, where p is prime.
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1
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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
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OFFSET
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1,1
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COMMENTS
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a(11)-a(26) from Chuck Gaydos.
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LINKS
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EXAMPLE
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a(7) = 360 because 360 has a record-breaking 24 divisors and 360 = p^2-1, where p = 19 is prime.
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MATHEMATICA
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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 *)
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PROG
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(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
n = divisor_count(p**2-1)
if n > nmax:
nmax = n
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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