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A274877 Least number, m, such that m^2 is expressible in just n ways as (p+1)(q+1) where p and q are distinct primes. 2
1, 6, 18, 12, 24, 60, 156, 84, 144, 120, 816, 336, 360, 1224, 840, 924, 2184, 1800, 2640, 7200, 1260, 3960, 7140, 8400, 3780, 5040, 2520, 9360, 12600, 20160, 11340, 10080, 15120, 19656, 16380, 41580, 18480, 48720, 34320, 25200, 54600, 27720, 87360, 134640, 60060, 73920, 32760, 43680, 159600, 143640, 55440, 85800, 96096, 65520, 131040, 120120, 157080, 154440, 98280, 191520, 166320 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Records: 1, 6, 12, 24, 60, 84, 120, 336, 360, 840, ..., .

LINKS

Table of n, a(n) for n=0..60.

EXAMPLE

a(0) = 1 since 1 is not expressible as (p+1)(q+1), in fact no odd number is expressible this way;

a(1) = 6 since 6^2 = 36 = (2+1)(11+1);

a(2) = 18 since 18^2 = 324 = (2+1)(107+1) = (5+1)(53+1);

a(3) = 12 since 12^2 = 144 = (2+1)(47+1) = (5+1)(23+1) = (7+1)(17+1); etc.

MATHEMATICA

(* first compute A274876: f[n_] := f[n] = Block[{c = 0, p = 2}, While[p < 2n -1, If[ PrimeQ[(2n)^2/(p +1) -1], c++]; p = NextPrime@ p]; c]; f[0] = 1; then *) Table[(2Select[ Range@ 5000, f@# == n &])[[1]], {n, 0, 10}]

CROSSREFS

Cf. A274848, A274877.

Sequence in context: A078741 A248461 A129870 * A091014 A097370 A252897

Adjacent sequences:  A274874 A274875 A274876 * A274878 A274879 A274880

KEYWORD

nonn

AUTHOR

Zak Seidov and Robert G. Wilson v, Jul 10 2016

STATUS

approved

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Last modified July 19 08:49 EDT 2019. Contains 325155 sequences. (Running on oeis4.)