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A094191
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a(n) = smallest number that occurs exactly n times as a difference between two positive squares.
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0
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3, 15, 45, 96, 192, 240, 576, 480, 720, 960, 12288, 1440, 3600, 3840, 2880, 3360, 20736, 5040, 147456, 6720, 11520, 14400, 50331648, 10080, 25920, 245760, 25200, 26880, 3221225472, 20160, 57600, 30240, 184320, 3932160, 103680, 40320, 129600, 2985984, 737280, 60480, 13194139533312, 80640, 52776558133248, 430080, 100800, 251658240, 84934656, 110880, 921600, 181440
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Related to A005179, "Smallest number with exactly n divisors", with which it shares a lot of common terms (in different positions).
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LINKS
| Johan Claes, homepage.
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EXAMPLE
| a(1)=3 because there is only one difference of positive squares which equals 3 (2^2-1^1).
a(2)=15 because 15 = 4^2-1^2 = 8^2-7^2.
a(3)=45 because 45 = 7^2-2^2 = 9^2-6^2 = 23^2-22^2.
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MATHEMATICA
| 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}] (from Robert G. Wilson v Jun 04 2004)
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PROG
| (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)
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CROSSREFS
| Cf. A068314.
Sequence in context: A177146 A161400 A112810 * A050534 A048099 A030505
Adjacent sequences: A094188 A094189 A094190 * A094192 A094193 A094194
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KEYWORD
| nonn
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AUTHOR
| Johan Claes (johan.claes(AT)luc.ac.be), Jun 02 2004
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EXTENSIONS
| Edited by Don Reble (djr(AT)nk.ca) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 04 2004
Further terms from Johan Claes (johan.claes(AT)luc.ac.be), Jun 07 2004
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