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A195382 Numbers such that the difference between the sum of the even divisors and the sum of the odd divisors is prime. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 06:12 EST 2022. Contains 350444 sequences. (Running on oeis4.)