A218392 Primitive triangle numbers as defined in A218243.

60, 150, 200, 780, 1530, 1690, 1950, 2040, 2100, 2730, 2860, 3570, 4056, 4200, 4350, 4624, 5100, 5460, 8120, 8250, 8670, 8750, 10812, 11050, 11900, 12180, 13260, 13650, 14060, 14430, 14760, 15540, 17220, 17850, 18564, 19240, 23400, 24420, 26100, 26520, 27880, 29172, 30000

Offset

1,1

Comments

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.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Example

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

Prog

(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)

Crossrefs

Sequence in context: A211332 A039497 A218243 * A135199 A112065 A252018

Adjacent sequences: A218389 A218390 A218391 * A218393 A218394 A218395

Keyword

nonn

Author

M. F. Hasler, Oct 27 2012

Status

approved