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A058063
Number of prime factors (when counted with multiplicity) of sigma(n), the sum of divisors of n.
14
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, 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, 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
OFFSET
1,3
FORMULA
a(n) = A001222(A000203(n)).
From Antti Karttunen, Feb 12 2020: (Start)
Additive with a(p^e) = A001222(A000203(p^e)) = A001222(1 + p + p^2 + ... + p^e).
a(n) = A000120(A332221(n)).
(End)
EXAMPLE
n=35, sigma(35) = 35 + 5 + 7 + 1 = 48 = 2*2*2*2*3, so a(35)=5.
MAPLE
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
MATHEMATICA
Array[PrimeOmega@ DivisorSigma[1, #] &, 105] (* Michael De Vlieger, Nov 08 2017 *)
PROG
(PARI) a(n) = bigomega(sigma(n)); \\ Michel Marcus, Nov 07 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 23 2000
EXTENSIONS
Offset corrected by Antti Karttunen, Nov 07 2017
STATUS
approved