A352420 Number of distinct prime factors of sigma_n(n).
0, 1, 2, 3, 3, 4, 3, 2, 3, 5, 6, 8, 5, 5, 8, 6, 3, 8, 5, 11, 9, 7, 8, 10, 8, 8, 10, 12, 7, 13, 7, 11, 15, 10, 15, 11, 7, 8, 11, 10, 6, 14, 8, 14, 14, 11, 10, 17, 6, 21, 15, 16, 8, 18, 16, 15, 16, 6, 9, 22, 8, 10, 17, 13, 17, 17, 7, 17, 20, 17, 8, 23, 4, 13, 21
Offset: 1
Keywords
Examples
a(5) = 3; a(5) = omega(sigma_5(5)) = omega(1^5+5^5) = omega(3126) = 3.
Links
- Daniel Suteu, Table of n, a(n) for n = 1..120
Programs
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Maple
A342420 := proc(n) A001221(A023887(n)) ; # reuses other codes end proc: seq(A342420(n),n=1..20) ; # R. J. Mathar, Apr 06 2022
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Mathematica
Table[PrimeNu[DivisorSigma[n, n]], {n, 30}] -
PARI
a(n) = omega(sigma(n, n)); \\ Daniel Suteu, Mar 23 2022
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Python
from sympy import primefactors, factorint def A352420(n): return len(set().union(*(primefactors((p**((e+1)*n)-1)//(p**n-1)) for p, e in factorint(n).items()))) # Chai Wah Wu, Mar 24 2022
Extensions
a(67)-a(75) from Daniel Suteu, Mar 23 2022