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A117949
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Index of pentagonal numbers whose sum of divisors is square.
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1
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0, 1, 4, 7, 12, 21, 23, 27, 31, 71, 79, 89, 151, 168, 199, 223, 232, 239, 263, 311, 324, 336, 345, 359, 390, 463, 479, 497, 540, 599, 743, 751, 823, 858, 863, 911, 991, 1031, 1063, 1103, 1151, 1302, 1303, 1343, 1399, 1471, 1540, 1583, 1687, 1759, 1802, 1823
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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). A000326 Pentagonal numbers: n(3n-1)/2. A000203 sigma(n) = sum of divisors of n. Also called sigma_1(n). A074285 Sum of the divisors of n-th triangular number. A117948 Sum of the divisors of pentagonal numbers.
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FORMULA
| n such that A117948(n) is in A000290. n such that SUM[d|A000326(n)] d is in A000290. n such that A000203(A000326(n)) is in A000290. n such that SUM[d|(n*(3*n-1)/2)] d = k^2 for integer k.
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EXAMPLE
| a(1) = 1 because sigma[1*(3*1-1)/2)] = 1 = 1^2.
a(2) = 4 because sigma[4*(3*4-1)/2)] = 36 = 6^2.
a(3) = 7 because sigma[7*(3*7-1)/2)] = 144 = 12^2.
a(4) = 12 because sigma[12*(3*12-1)/2)] = 576 = 24^2.
a(5) = 21 because sigma[21*(3*21-1)/2)] = 1024 = 32^2.
a(6) = 23 because sigma[23*(3*23-1)/2)] = 1296 = 36^2.
a(7) = 27 because sigma[27*(3*27-1)/2)] = 3600 = 60^2.
a(8) = 31 because sigma[31*(3*31-1)/2)] = 2304 = 48^2.
a(9) = 71 because sigma[71*(3*71-1)/2)] = 11664 = 108^2.
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MAPLE
| with(numtheory): a:=proc(n) if type(sqrt(sigma(n*(3*n-1)/2)), integer)=true then n else fi end: seq(a(n), n=0..2200); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2006
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CROSSREFS
| Cf. A000203, A000217, A000290, A000326, A074285, A083675, A117948.
Sequence in context: A022809 A188554 A020732 * A010901 A187211 A023624
Adjacent sequences: A117946 A117947 A117948 * A117950 A117951 A117952
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 04 2006
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 06 2006
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