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Search: id:A116990
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| A116990 |
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Index of triangular numbers whose sum of divisors is square. |
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+0
1
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| 0, 1, 2, 11, 20, 40, 68, 92, 212, 236, 253, 266, 321, 328, 452, 582, 589, 596, 668, 695, 716, 782, 788, 836, 928, 932, 970, 991, 1012, 1065, 1076, 1173, 1264, 1300, 1336, 1388, 1436, 1490, 1549, 1796, 1854, 1927, 1995, 2159, 2228, 2252, 2468, 2545, 2588
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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See also: A000217 Triangular numbers: a(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+...+n. A074285 Sum of the divisors of n-th triangular number. A083675 Triangular number for which the sum of the proper divisors is also a triangular number. A000203 sigma(n) = sum of divisors of n. Also called sigma_1(n).
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FORMULA
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n such that A074285(n) is in A000290. n such that SUM[d|A000217(n)] d is in A000290. n such that A000203(A000217(n)) is in A000290. n such that SUM[d|n*(n+1)/2] d = k^2 for integer k.
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EXAMPLE
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a(1) = 1 because sigma[1*(1+1)/2] = 1 = 1^2.
a(2) = 2 because sigma[2*(2+1)/2] = sigma[3] = 1 + 3 = 4 = 2^2.
a(3) = 11 because sigma[11*(11+1)/2] = sigma[66] = 1 + 2 + 3 + 6 + 11 + 22 + 33 + 66 = 144 = 12^2.
a(4) = 20 because sigma[20*(20+1)/2] = sigma[210] = 576 = 24^2.
a(5) = 40 because sigma[40*(40+1)/2] = sigma[820] = 1764 = 42^2.
a(6) = 68 because sigma[68*(68+1)/2] = sigma[2346] = 5184 = 72^2.
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MAPLE
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with(numtheory): a:=proc(n) if type(sqrt(sigma(n*(n+1)/2)), integer)=true then n else fi end: seq(a(n), n=0..3100); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2006
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CROSSREFS
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Cf. A000203, A000217, A000290, A074285, A083675.
Sequence in context: A067670 A017185 A092595 this_sequence A146087 A064975 A115095
Adjacent sequences: A116987 A116988 A116989 this_sequence A116991 A116992 A116993
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KEYWORD
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easy,nonn,less
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 04 2006
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2006
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