A136565 - OEIS

%I #21 Sep 07 2018 03:07:45

%S 0,1,1,2,1,1,1,3,2,1,1,3,1,1,1,4,1,3,1,3,1,1,1,4,2,1,3,3,1,1,1,5,1,1,

%T 1,2,1,1,1,4,1,1,1,3,3,1,1,5,2,3,1,3,1,4,1,4,1,1,1,3,1,1,3,6,1,1,1,3,

%U 1,1,1,5,1,1,3,3,1,1,1,5,4,1,1,3,1,1,1,4,1,3,1,3,1,1,1,6,1,3,3,2,1,1,1,4,1

%N a(n) = sum of the distinct values making up the exponents in the prime-factorization of n.

%C a(n) = A088529(n) = A181591(n) for n: 2 <= n < 24. - _Reinhard Zumkeller_, Nov 01 2010

%H Antti Karttunen, <a href="/A136565/b136565.txt">Table of n, a(n) for n = 1..65537</a> (terms 1..1000 from Diana Mecum)

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F a(n) = A066328(A181819(n)). - _Antti Karttunen_, Sep 06 2018

%e 120 = 2^3 * 3^1 * 5^1. The exponents of the prime factorization are therefore 3,1,1. The distinct values which equal these exponents are 1 and 3. So a(120) = 1+3 = 4.

%t Join[{0},Table[Total[Union[Transpose[FactorInteger[n]][[2]]]],{n,2,110}]] (* _Harvey P. Dale_, Jun 23 2013 *)

%o (PARI) A136565(n) = vecsum(apply(primepi,factor(factorback(apply(e->prime(e),(factor(n)[,2]))))[,1])); \\ _Antti Karttunen_, Sep 06 2018

%Y Cf. A066328, A071625, A136566, A136568, A181819.

%K nonn

%O 1,4

%A _Leroy Quet_, Jan 07 2008

%E More terms from _Diana L. Mecum_, Jul 17 2008