

A108815


Indices of triangular numbers which are products of 3 primes.


6



7, 9, 11, 12, 14, 17, 18, 19, 21, 25, 28, 29, 30, 33, 34, 38, 41, 42, 43, 52, 57, 66, 67, 70, 78, 85, 86, 93, 94, 97, 101, 102, 109, 113, 118, 121, 122, 130, 133, 137, 138, 141, 142, 145, 148, 158, 163, 172, 173, 177, 181, 190, 201, 202, 205, 211, 213, 214, 217, 218
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OFFSET

1,1


COMMENTS

Indices of 3almost prime triangular numbers.


LINKS



FORMULA

{a(n)} = {k such that A001222(A000217(k)) = 3}. {a(n)} = {k such that k*(k+1)/2 has exactly 3 prime factors, with multiplicity}. {a(n)} = {k such that A000217(k) is an element of A014612}.
n such that n*(n+1)/2 is an element of A014612. n such that A000217(n) is an element of A014612. n such that C(n+1, 2) is an element of A014612.


EXAMPLE

a(1) = 7 because T(7) = TriangularNumber(7) = 7*(7+1)/2 = 28 = 2^2 * 7 is a 3almost prime.
a(2) = 9 because T(9) = 9*(9+1)/2 = 45 = 3^2 * 5 is a 3almost prime.
a(3) = 11 because T(11) = 11*(11+1)/2 = 66 = 2 * 3 * 11.
a(31) = 101 because T(101) = 101*(101+1)/2 = 5151 = 3 * 17 * 101.
a(49) = 173 because T(173) = 173*(173+1)/2 = 15051 = 3 * 29 * 173.


MATHEMATICA

Select[Range[225], Plus @@ Last /@ FactorInteger[ #*(# + 1)/2] == 3 &] (* Ray Chandler, Jul 16 2005 *)


PROG

(PARI) issemi(n)=bigomega(n)==2
is(n)=if(isprime(n/gcd(n, 2)), issemi((n+1)/gcd(n+1, 2)), isprime((n+1)/gcd(n+1, 2)) && issemi(n/gcd(n, 2))) \\ Charles R Greathouse IV, Feb 05 2017


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



