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A080982
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Smallest k such that the k-th triangular number has n^2 as divisor.
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4
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1, 7, 8, 31, 24, 8, 48, 127, 80, 24, 120, 63, 168, 48, 99, 511, 288, 80, 360, 224, 98, 120, 528, 512, 624, 168, 728, 735, 840, 224, 960, 2047, 242, 288, 49, 1215, 1368, 360, 675, 1024, 1680, 440, 1848, 1088, 324, 528, 2208, 512, 2400, 624, 288, 1183, 2808, 728
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OFFSET
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1,2
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LINKS
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FORMULA
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a(2^k) = 2^(2*k+1) - 1.
a(m) = m^2 - 1 for odd prime powers m.
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PROG
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(Haskell)
import Data.List (findIndex)
import Data.Maybe (fromJust)
a080982 n = (+ 1) $ fromJust $
findIndex ((== 0) . (`mod` (n ^ 2))) $ tail a000217_list
(Python 3.8+)
from itertools import combinations
from sympy import factorint
from sympy.ntheory.modular import crt
k = 2*n**2
plist = [p**q for p, q in factorint(k).items()]
return k-1 if len(plist) == 1 else min(min(crt([m, k//m], [0, -1])[0], crt([k//m, m], [0, -1])[0]) for m in (prod(d) for l in range(1, len(plist)//2+1) for d in combinations(plist, l))) # Chai Wah Wu, Jun 13 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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