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A274876 The number of ways (2n)^2 is expressible as (p+1)(q+1) where p and q are distinct primes. 2
0, 0, 1, 0, 0, 3, 0, 1, 2, 0, 0, 4, 0, 1, 1, 1, 0, 4, 0, 2, 3, 1, 0, 4, 0, 1, 1, 2, 0, 5, 0, 1, 2, 1, 1, 4, 0, 1, 3, 1, 0, 7, 0, 2, 4, 0, 0, 4, 0, 2, 3, 1, 0, 2, 0, 2, 0, 0, 0, 9, 0, 0, 2, 0, 0, 5, 0, 3, 0, 2, 0, 8, 0, 0, 2, 2, 2, 6, 0, 2, 2, 1, 0, 6, 0, 1, 1, 2, 0, 8, 1, 1, 1, 0, 0, 2, 0, 1, 0, 4, 0, 4, 0, 2, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

No odd number squared is expressible as (p+1)(q+1) where p and q are distinct primes, since q must be odd and therefore (q+1) is even.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 0 since 2 is not expressible as (p+1)(q+1); same for a(2); a(3) = 1 since 6^2 = 36 = (2+1)(11+1); a(6) = 3 since 12^2 = 144 = (2+1)(47+1) = (5+1)(23+1) = (7+1)(17+1); a(9) = 2 since 18^2 = 324 = (2+1)(107+1) = (5+1)(53+1); etc.

MATHEMATICA

f[n_] := Block[{c = 0, p = 2}, While[p < 2n -1, If[ PrimeQ[(2n)^2/(p +1) -1], c++]; p = NextPrime@ p]; c]; Array[f, 105]

PROG

(PARI) a(n)=sumdiv(4*n^2, d, d<2*n && isprime(d-1) && isprime(4*n^2/d-1)) \\ Charles R Greathouse IV, Jul 10 2016

CROSSREFS

Cf. A274848, A274877.

Sequence in context: A303301 A160499 A329272 * A065718 A025428 A199176

Adjacent sequences:  A274873 A274874 A274875 * A274877 A274878 A274879

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified February 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)