A185642 Nearest integer to average of distinct prime factors of n.

2, 3, 2, 5, 3, 7, 2, 3, 4, 11, 3, 13, 5, 4, 2, 17, 3, 19, 4, 5, 7, 23, 3, 5, 8, 3, 5, 29, 3, 31, 2, 7, 10, 6, 3, 37, 11, 8, 4, 41, 4, 43, 7, 4, 13, 47, 3, 7, 4, 10, 8, 53, 3, 8, 5, 11, 16, 59, 3, 61, 17, 5, 2, 9, 5, 67, 10, 13, 5, 71, 3, 73, 20, 4, 11, 9, 6, 79

Offset: 2

Author

Arkadiusz Wesolowski, Sep 11 2013

Keywords

• nonn

Comments

a(n) = n if and only if n is prime.

Examples

			a(12) = 3, since the prime factors of 12 are 2 and 3, the average of 2 and 3 is 2.5, and the nearest integer to 2.5 is 3 (the larger number is chosen when the average is a half-integer).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..1000
• Index to divisibility sequences

Crossrefs

Cf. A001221, A008472.

Programs

Mathematica

Table[Floor[Mean[FactorInteger[n][[All,1]]]+1/2],{n,2,80}] (* Harvey P. Dale, Sep 23 2016 *)

PARI

for(n=2, 79, o=omega(n); s=sum(i=1, o, factor(n)[, 1][i]); print1(round(s/o), ", "));

Formula

a(n) = round(A008472(n)/A001221(n)).