The On-Line Encyclopedia of Integer Sequences (OEIS)

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A270470

Integers n such that A001654(n) is divisible by n*(n+1)/2.
(history; published version)

#9 by N. J. A. Sloane at Sun Mar 20 12:57:48 EDT 2016

STATUS

proposed

approved

#8 by Michael De Vlieger at Sat Mar 19 09:09:30 EDT 2016

STATUS

editing

proposed

#7 by Michael De Vlieger at Sat Mar 19 09:09:27 EDT 2016

MATHEMATICA

nn = 4800; Function[k, Select[Range@ nn, Divisible[k[[# + 1]], # (# + 1)/2] &]]@ LinearRecurrence[{2, 2, -1}, {0, 1, 2}, nn + 1] (* Michael De Vlieger, Mar 19 2016, after Vladimir Joseph Stephan Orlovsky at A001654 *)

STATUS

proposed

editing

#6 by Altug Alkan at Thu Mar 17 14:44:40 EDT 2016

STATUS

editing

proposed

#5 by Altug Alkan at Thu Mar 17 14:38:34 EDT 2016

COMMENTS

Odd terms of this sequence are prime most of the time. Odd composite terms of this sequence are 1, 323, 575, 6479, 7055, ...

#4 by Altug Alkan at Thu Mar 17 14:25:35 EDT 2016

EXAMPLE

3 is a term because (1^2 + 1^2 + 2^2) / (1 + 2 + 3) = 1.

10 is a term because (1^2 + 1^2 + 2^2 + 3^2 + 5^2 + 8^2 + 13^2 + 21^2 + 34^2 + 55^2) / (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) = 89.

#3 by Altug Alkan at Thu Mar 17 14:21:06 EDT 2016

CROSSREFS

Cf. A000217, A001654.

#2 by Altug Alkan at Thu Mar 17 14:19:34 EDT 2016

NAME

allocated for Altug AlkanIntegers n such that A001654(n) is divisible by n*(n+1)/2.

DATA

1, 3, 10, 23, 24, 47, 60, 107, 108, 167, 180, 240, 250, 323, 383, 503, 540, 575, 600, 647, 660, 683, 768, 863, 1008, 1103, 1200, 1223, 1320, 1367, 1620, 1728, 1800, 1860, 2160, 2207, 2447, 2520, 2687, 2688, 2736, 3000, 3023, 3060, 3300, 3360, 3527, 3528, 3744, 3863, 3888, 4200, 4703, 4800

OFFSET

1,2

PROG

(PARI) a(n) = fibonacci(n)*fibonacci(n+1);

for(n=1, 1e4, if(a(n) % (n*(n+1)/2) ==0, print1(n, ", ")));

KEYWORD

allocated

nonn

AUTHOR

Altug Alkan, Mar 17 2016

STATUS

approved

editing

#1 by Altug Alkan at Thu Mar 17 14:19:34 EDT 2016

NAME

allocated for Altug Alkan

KEYWORD

allocated

STATUS

approved