A099910 Number of distinct prime-factors of ((prime(n)*(prime(n+1)-1)+(prime(n)-1)*prime(n+1))/2).

1, 1, 2, 1, 2, 2, 2, 1, 2, 3, 2, 1, 3, 1, 2, 1, 2, 2, 2, 3, 2, 2, 4, 3, 1, 2, 2, 3, 3, 2, 2, 3, 2, 1, 2, 3, 3, 3, 2, 3, 3, 1, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 3, 2, 1, 2, 3, 4, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 4, 4, 2, 2, 2, 3, 2, 3, 1, 1, 3, 1, 4, 3, 1, 4, 3, 1, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 1, 1, 3, 1, 3, 3

Offset

2,3

Comments

a(n) = A001221(A099909(n)).

Links

G. C. Greubel, Table of n, a(n) for n = 2..5000

Mathematica

dpf[{a_, b_}]:=PrimeNu[((a(b-1))+(a-1)b)/2]; dpf/@Partition[Prime[ Range[ 2, 110]], 2, 1] (* Harvey P. Dale, Nov 16 2011 *)

Prog

(PARI) a(n)=omega(((prime(n)*(prime(n+1)-1)+(prime(n)-1)*prime(n+1))/2)) \\ Michel Marcus, May 16 2017

Crossrefs

Cf. A099911, A098142 (a(n) is 1).

Sequence in context: A362028 A303401 A327491 * A376780 A213325 A043555

Adjacent sequences: A099907 A099908 A099909 * A099911 A099912 A099913

Keyword

nonn

Author

Reinhard Zumkeller, Oct 29 2004

Status

approved