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A352420 Number of distinct prime factors of sigma_n(n).

%I A352420 #36 Apr 06 2022 05:53:22
%S A352420 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,
%T A352420 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,
%U A352420 16,6,9,22,8,10,17,13,17,17,7,17,20,17,8,23,4,13,21
%N A352420 Number of distinct prime factors of sigma_n(n).
%H A352420 Daniel Suteu, <a href="/A352420/b352420.txt">Table of n, a(n) for n = 1..120</a>
%F A352420 a(n) = omega(sigma_n(n)) = A001221(A023887(n)).
%e A352420 a(5) = 3; a(5) = omega(sigma_5(5)) = omega(1^5+5^5) = omega(3126) = 3.
%p A352420 A342420 := proc(n)
%p A352420     A001221(A023887(n)) ; # reuses other codes
%p A352420 end proc:
%p A352420 seq(A342420(n),n=1..20) ; # _R. J. Mathar_, Apr 06 2022
%t A352420 Table[PrimeNu[DivisorSigma[n, n]], {n, 30}]
%o A352420 (PARI) a(n) = omega(sigma(n, n)); \\ _Daniel Suteu_, Mar 23 2022
%o A352420 (Python)
%o A352420 from sympy import primefactors, factorint
%o A352420 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
%Y A352420 Cf. A001221 (omega), A023887 (sigma_n(n)).
%Y A352420 Cf. A064165, A347718.
%K A352420 nonn
%O A352420 1,3
%A A352420 _Wesley Ivan Hurt_, Mar 21 2022
%E A352420 a(67)-a(75) from _Daniel Suteu_, Mar 23 2022