A126247 a(n) is the number of triangular numbers, from among (T(1), T(2), T(3), ..., T(n)), which are coprime to T(n), where T(n) = n(n+1)/2 is the n-th triangular number.

1, 1, 1, 2, 1, 2, 3, 1, 2, 6, 1, 2, 9, 1, 2, 8, 5, 6, 5, 1, 4, 18, 3, 3, 13, 7, 4, 10, 5, 6, 15, 3, 8, 12, 2, 6, 33, 9, 3, 12, 9, 10, 17, 3, 8, 42, 7, 6, 21, 9, 6, 22, 17, 9, 9, 5, 16, 54, 5, 6, 57, 13, 8, 17, 9, 18, 29, 8, 9, 30, 11, 12, 69, 13, 7, 17, 12, 22, 23, 8, 26, 78, 9, 8, 43, 25, 12, 36

Offset

1,4

Links

Table of n, a(n) for n=1..88.

Example

T(10) = 10*11/2 = 55. The six triangular numbers which are coprime to 55 and are <= 55 are T(1)=1, T(2)=3, T(3)=6, T(6)=21, T(7)=28 and T(8)=36. So a(10) = 6.

Maple

a:=proc(n) local ct, i: ct:=0: for i from 1 to n do if gcd(i*(i+1)/2, n*(n+1)/2)=1 then ct:=ct+1 else ct:=ct fi: od: ct: end: seq(a(n), n=1..100); # Emeric Deutsch, Mar 24 2007

Prog

(PARI) a(n) = sum(k=1, n, gcd(n*(n+1)/2, k*(k+1)/2) == 1); \\ Michel Marcus, Feb 01 2019

Crossrefs

Cf. A000217.

Sequence in context: A263683 A087730 A263736 * A213999 A374411 A249026

Adjacent sequences: A126244 A126245 A126246 * A126248 A126249 A126250

Keyword

nonn

Author

Leroy Quet, Mar 08 2007

Extensions

More terms from Emeric Deutsch, Mar 24 2007

Status

approved