cp's OEIS Frontend

A058063 Number of prime factors (when counted with multiplicity) of sigma(n), the sum of divisors of n.

%I A058063 #22 Feb 13 2020 02:50:40
%S A058063 0,1,2,1,2,3,3,2,1,3,3,3,2,4,4,1,3,2,3,3,5,4,4,4,1,3,4,4,3,5,5,3,5,4,
%T A058063 5,2,2,4,4,4,3,6,3,4,3,5,5,3,2,2,5,3,4,5,5,5,5,4,4,5,2,6,4,1,4,6,3,4,
%U A058063 6,6,5,3,2,3,3,4,6,5,5,3,2,4,4,6,5,4,5,5,4,4,5,5,7,6,5,5,3,3,4,2,3,6,4,4,7
%N A058063 Number of prime factors (when counted with multiplicity) of sigma(n), the sum of divisors of n.
%H A058063 Antti Karttunen, <a href="/A058063/b058063.txt">Table of n, a(n) for n = 1..16384</a>
%H A058063 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F A058063 a(n) = A001222(A000203(n)).
%F A058063 From _Antti Karttunen_, Feb 12 2020: (Start)
%F A058063 Additive with a(p^e) = A001222(A000203(p^e)) = A001222(1 + p + p^2 + ... + p^e).
%F A058063 a(n) = A000120(A332221(n)).
%F A058063 (End)
%e A058063 n=35, sigma(35) = 35 + 5 + 7 + 1 = 48 = 2*2*2*2*3, so a(35)=5.
%p A058063 with(numtheory):a:=proc(n) if n=0 then 0 else bigomega(sigma(n)) fi end: seq(a(n), n=1..105); # _Zerinvary Lajos_, Apr 11 2008
%t A058063 Array[PrimeOmega@ DivisorSigma[1, #] &, 105] (* _Michael De Vlieger_, Nov 08 2017 *)
%o A058063 (PARI) a(n) = bigomega(sigma(n)); \\ _Michel Marcus_, Nov 07 2017
%Y A058063 Cf. A000120, A000203, A001222, A331750, A332221.
%K A058063 nonn
%O A058063 1,3
%A A058063 _Labos Elemer_, Nov 23 2000
%E A058063 Offset corrected by _Antti Karttunen_, Nov 07 2017