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A060462 n! is divisible by n*(n+1)/2. 15
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

n! / (n-th triangular number) is an integer.

a(k) = A072668(k) for k>0.

REFERENCES

J. D. E. Konhauser et al., Which Way Did The Bicycle Go?, Problem 98, pp. 29; 145-146, MAA Washington DC, 1996.

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..2000

EXAMPLE

5*4*3*2*1=120 is divisible by 5 + 4 + 3 + 2 + 1 = 15.

MAPLE

for n from 1 to 300 do if n! mod (n*(n+1)/2) = 0 then printf(`%d, `, n) fi:od:

MATHEMATICA

Select[Range[94], Mod[#!, #*(# + 1)/2] == 0 &] (* Jayanta Basu, Apr 24 2013 *)

PROG

(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

CROSSREFS

Sequence in context: A299542 A144724 A196990 * A072668 A249433 A300737

Adjacent sequences:  A060459 A060460 A060461 * A060463 A060464 A060465

KEYWORD

nonn

AUTHOR

Michel ten Voorde Apr 09 2001

EXTENSIONS

Corrected and extended by Henry Bottomley and James A. Sellers, Apr 11 2001

STATUS

approved

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Last modified April 20 06:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)