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%I #31 Nov 16 2017 02:53:29
%S 1,2,0,2,0,4,0,0,0,4,0,4,0,0,0,2,0,4,0,0,0,4,0,2,0,0,0,4,0,8,0,0,0,2,
%T 0,4,0,0,0,4,0,8,0,0,0,2,0,2,0,0,0,4,0,2,0,0,0,4,0,8,0,0,0,0,0,4,0,0,
%U 0,8,0,4,0,0,0,2,0,8,0,0,0,4,0,4,0,0,0,4,0,6
%N Number of divisors k of n such that (n + k^2)/k is a prime.
%C Except for the single case of a(1)=1 all terms are even. - _Robert G. Wilson v_, Feb 25 2017
%C First occurrence of 2k: 3, 2, 6, 90, 30, 390, 690, 420, 210, 4290, 3990, 8778, 2310, 3570, 4830, 11550, 38850, 84630, 66990, 79170, 39270, 30030, 51870, 46410, 43890, ..., . - _Robert G. Wilson v_, Feb 25 2017
%H Robert G. Wilson v, <a href="/A282849/b282849.txt">Table of n, a(n) for n = 1..10000</a>
%H Michael De Vlieger, <a href="/A282849/a282849.txt">Records and indices of records</a>.
%F a(1) = 1; for n > 0: a(2n) = 2*A088627(n), a(2n + 1) = 0.
%e a(6) = 4 because (6 + 1^2)/1 = 7 is prime, (6 + 2^2)/2 = 5 is prime, (6 + 3^2)/3 = 5 is prime, (6 + 6^2)/6 = 7 is prime, where 1, 2, 3 and 6 are divisors of 6.
%t f[n_] := Block[{d = Divisors@ n}, Length@ Select[d, PrimeQ[(n + #^2)/#] &]]; Array[f, 105] (* _Robert G. Wilson v_, Feb 25 2017 *)
%t Table[DivisorSum[n, 1 &, PrimeQ[(n + #^2)/#] &], {n, 105}] (* _Michael De Vlieger_, Nov 15 2017 *)
%o (PARI) a(n) = sumdiv(n, k, isprime((n+k^2)/k)); \\ _Michel Marcus_, Feb 26 2017
%Y Cf. A088627 (number of divisors k of n such that (n + 2*k^2)/k is prime), A047255.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Feb 24 2017
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