A069904 Number of prime factors of n-th triangular number (with multiplicity).

0, 1, 2, 2, 2, 2, 3, 4, 3, 2, 3, 3, 2, 3, 5, 4, 3, 3, 3, 4, 3, 2, 4, 5, 3, 4, 5, 3, 3, 3, 5, 6, 3, 3, 5, 4, 2, 3, 5, 4, 3, 3, 3, 5, 4, 2, 5, 6, 4, 4, 4, 3, 4, 5, 5, 5, 3, 2, 4, 4, 2, 4, 8, 7, 4, 3, 3, 4, 4, 3, 5, 5, 2, 4, 5, 4, 4, 3, 5, 8, 5, 2, 4, 5, 3, 3, 5, 4, 4, 5

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = A001222(A000217(n)).

From Antti Karttunen, Oct 07 2017: (Start)

a(n) = (A001222(n)+A001222(n+1))-1.

a(n) = A001222(A278253(n)). (End)

From Alois P. Heinz, Aug 05 2019: (Start)

a(n) = 2 <=> n in { A164977 }.

a(n) = 3 <=> n in { A108815 }.

a(n) = 4 <=> n in { A114435 }.

a(n) = 5 <=> n in { A114436 }.

a(n) = 6 <=> n in { A114437 }.

a(n) = 7 <=> n in { A240527 }.

a(n) = 8 <=> n in { A240528 }.

a(n) = 9 <=> n in { A240529 }.

a(n) = 10 <=> n im { A101745 }. (End)

Example

A000217(8) = 8*(8+1)/2 = 36 = 2*2*3*3, therefore a(8) = 4.

Mathematica

Array[Plus@@Last/@FactorInteger[ #*(#+1)/2]&, 33] (* Vladimir Joseph Stephan Orlovsky, Feb 28 2010 *)

Prog

(PARI) A069904(n) = bigomega((n*(n+1))/2); \\ Antti Karttunen, Oct 07 2017

Crossrefs

Cf. A069901, A069902, A069903, A092405, A101745, A108815, A114435, A114436, A114437, A164977, A240527, A240528, A240529, A278253.

Sequence in context: A221530 A262944 A322789 * A164978 A119789 A025424

Adjacent sequences: A069901 A069902 A069903 * A069905 A069906 A069907

Keyword

nonn

Author

Reinhard Zumkeller, Apr 10 2002

Status

approved