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A060462
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Integers k such that k! is divisible by k*(k+1)/2.
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18
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1, 3, 5, 7, 8, 9, 11, 13, 14, 15, 17, 19, 20, 21, 23, 24, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 80, 81, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94
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OFFSET
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1,2
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COMMENTS
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k! / (k-th triangular number) is an integer.
Numbers k such that Sum_{j=1..k} j divides Product_{j=1..k} j.
k is a term iff k != p-1 with p is an odd prime (see De Koninck & Mercier reference).
The ratios obtained a(n)!/T(a(n)) = A108552(n). (End)
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REFERENCES
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Jean-Marie De Koninck & Armel Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 181 pp. 31 and 163, Ellipses, Paris, 2004.
Joseph D. E. Konhauser et al., Which Way Did The Bicycle Go?, Problem 98, pp. 29; 145-146, MAA Washington DC, 1996.
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LINKS
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EXAMPLE
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5 is a term because 5*4*3*2*1 = 120 is divisible by 5 + 4 + 3 + 2 + 1 = 15.
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MAPLE
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for n from 1 to 300 do if n! mod (n*(n+1)/2) = 0 then printf(`%d, `, n) fi:od:
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MATHEMATICA
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Select[Range[94], Mod[#!, #*(# + 1)/2] == 0 &] (* Jayanta Basu, Apr 24 2013 *)
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PROG
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(PARI) { f=1; t=0; n=-1; for (m=1, 4000, f*=m; t+=m; if (f%t==0, write("b060462.txt", n++, " ", m)); if (n==2000, break); ) } \\ Harry J. Smith, Jul 05 2009
(Python)
from sympy import composite
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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