A195382 Numbers such that the difference between the sum of the even divisors and the sum of the odd divisors is prime.

4, 8, 16, 18, 32, 50, 256, 512, 578, 1458, 2048, 3362, 4802, 6962, 8192, 10082, 15842, 20402, 31250, 34322, 55778, 57122, 59858, 167042, 171698, 293378, 524288, 559682, 916658, 982802, 1062882, 1104098, 1158242, 1195058, 1367858, 1407842, 1414562

Offset

1,1

Comments

Note that these are all even numbers. The odd numbers, producing the negative of a prime, are all squares whose square roots are in A193070. - T. D. Noe, Sep 19 2011

Links

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

Example

The divisors of 18 are  { 1, 2, 3, 6, 9, 18}, and  (2 + 6 + 18) - (1 + 3 + 9) = 13  is prime. Hence 18 is in the sequence.

Maple

with(numtheory):for n from 2 by 2 to 200 do:x:=divisors(n):n1:=nops(x):s1:=0:s2:=0:for m from 1 to n1 do:if irem(x[m], 2)=1 then s1:=s1+x[m]:else s2:=s2+x[m]:fi:od: if type(s2-s1, prime)=true then printf(`%d, `, n): else fi:od:

Mathematica

f[n_] := Module[{d = Divisors[n], p}, p = Plus @@ Select[d, OddQ] - Plus @@ Select[d, EvenQ]; PrimeQ[p]]; Select[Range[2, 1000000, 2], f] (* T. D. Noe, Sep 19 2011 *)

Prog

(PARI) list(lim)=my(v=List(), t); forstep(n=3, sqrt(lim\2), 2, if(isprime(s=sigma(n^2)), listput(v, 2*n^2))); t=2; while((t*=2)<=lim, if(isprime(2*sigma(t/2)-1), listput(v, t))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Sep 18 2011

Crossrefs

Subsequence of A088827.

Cf. A002129, A113184.

Sequence in context: A070738 A055744 A141718 * A211413 A181310 A212110

Adjacent sequences: A195379 A195380 A195381 * A195383 A195384 A195385

Keyword

nonn

Author

Michel Lagneau, Sep 17 2011

Status

approved