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%I #15 Mar 18 2018 03:40:24
%S 3,15,45,96,192,240,576,480,720,960,12288,1440,3600,3840,2880,3360,
%T 20736,5040,147456,6720,11520,14400,50331648,10080,25920,245760,25200,
%U 26880,3221225472,20160,57600,30240,184320,3932160,103680,40320,129600,2985984,737280,60480,13194139533312,80640,9663676416,430080,100800,251658240,84934656,110880,921600,181440
%N a(n) = smallest positive number that occurs exactly n times as a difference between two positive squares.
%C Related to A005179, "Smallest number with exactly n divisors", with which it shares a lot of common terms (in different positions).
%C It appears that, for entries having prime index p > 3, the minimal solution is 2^(p+1)*3 for Sophie Germain primes p. The number 43 is not such a prime, and we have the smaller solution 2^30*3^2. - _T. D. Noe_, Mar 14 2018
%H T. D. Noe, <a href="/A094191/b094191.txt">Table of n, a(n) for n = 1..999</a>
%H Johan Claes, <a href="https://www.uhasselt.be/fiche_en?email=johan.claes">homepage</a>. [Broken link (unknown server) replaced with link to current user's "homepage". - _M. F. Hasler_, Mar 14 2018]
%e a(1)=3 because there is only one difference of positive squares which equals 3 (2^2-1^1).
%e a(2)=15 because 15 = 4^2-1^2 = 8^2-7^2.
%e a(3)=45 because 45 = 7^2-2^2 = 9^2-6^2 = 23^2-22^2.
%t s = Split[ Sort[ Flatten[ Table[ Select[ Table[ b^2 - c^2, {c, b - 1}], # < 500000 &], {b, 250000}]]]]; f[s_, p_] := Block[{l = Length /@ s}, If[ Position[l, p, 1, 1] != {}, d = s[[ Position[l, p, 1, 1][[1, 1]] ]] [[1]], d = 0]; d]; t = Table[ f[s, n], {n, 36}] (* _Robert G. Wilson v_, Jun 04 2004 *)
%o (PARI) {occurrences(d)=local(c,n,a);c=0;for(n=1,(d-1)\2,if(issquare(a=n^2+d),c++));c} {m=50;z=30000;v=vector(m,n,-1);for(d=1,z,k=occurrences(d);if(0<k&&k<=m&&v[k]<0,v[k]=d));for(n=1,m,print1(v[n],","))} \\ _Klaus Brockhaus_
%Y Cf. A068314.
%K nonn
%O 1,1
%A _Johan Claes_, Jun 02 2004
%E Edited by _Don Reble_ and _Klaus Brockhaus_, Jun 04 2004
%E Further terms from _Johan Claes_, Jun 07 2004
%E a(43) corrected by _T. D. Noe_, Mar 14 2018
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