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A218392 Primitive triangle numbers as defined in A218243. 2

%I #14 May 13 2013 01:54:22

%S 60,150,200,780,1530,1690,1950,2040,2100,2730,2860,3570,4056,4200,

%T 4350,4624,5100,5460,8120,8250,8670,8750,10812,11050,11900,12180,

%U 13260,13650,14060,14430,14760,15540,17220,17850,18564,19240,23400,24420,26100,26520,27880,29172,30000

%N Primitive triangle numbers as defined in A218243.

%C Triangle numbers A218243 are integers n = a*b*c such that the triangle with sides (a,b,c) has integer area. For any such n, n*k^3 is again an element of A218243 for any integer k>0. Terms in A218243 which are not of that form (with k>1) are called "primitive", and listed here.

%H Charles R Greathouse IV, <a href="/A218392/b218392.txt">Table of n, a(n) for n = 1..1000</a>

%e The term A218243(4)=480 is not in this sequence since 480 = 2^3*60 and 60 = A218243(1).

%e The number n=30000=A218243(67) is divisible by 10^3, but neither of n/2^3, n/5^3, n/10^3 is in A218243, therefore n is in this sequence.

%o (PARI) is_A218392(n)=is_A218243(n) || return; my(f=factor(n)); vecmax(f[,2])<3 || !fordiv(factorback(Mat(apply(t->[t[1],t[2]\3]~,Vec(f~)))~),d,d>1 & is_A218243(n/d^3) & return)

%K nonn

%O 1,1

%A _M. F. Hasler_, Oct 27 2012

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