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 A069904 Number of prime factors of n-th triangular number (with multiplicity). 13
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 7 07:50 EDT 2020. Contains 333292 sequences. (Running on oeis4.)