A123529 Denominator of average of prime factors of n.

1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 4, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 1, 1, 3, 2, 1, 5, 1, 1, 1, 3, 1, 4, 1, 4, 1, 2, 1, 1, 1, 2, 3, 1, 1, 3, 1, 1, 1, 3, 1, 5, 1, 2, 3, 3, 1, 1, 1, 5, 1, 2, 1, 2, 1, 2, 1, 4, 1, 4, 1, 1, 1, 2, 1, 6, 1, 3, 3, 2, 1, 3, 1, 4, 1, 2

Offset: 2

Author

Franklin T. Adams-Watters, Oct 02 2006

Keywords

• frac
• nonn

Comments

Prime factors counted with multiplicity. - Harvey P. Dale, Jun 20 2013

Positions of 1's are A078175. a(n) is a divisor of Omega(n) = A001222(n). The average of prime indices (as opposed to prime factors) of n is A326567(n)/A326568(n). - Gus Wiseman, Jul 18 2019

Links

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

Crossrefs

See A123528 for more formulas and references.

Cf. A078174, A078175, A112798, A316413, A326567/A326568, A326619/A326620, A326621.

Programs

Mathematica

Table[Denominator[Mean[Flatten[Table[#[[1]],{#[[2]]}]&/@ FactorInteger[ n]]]],{n,110}] (* Harvey P. Dale, Jun 20 2013 *)