A352420 - OEIS

%I #36 Apr 06 2022 05:53:22

%S 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 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 16,6,9,22,8,10,17,13,17,17,7,17,20,17,8,23,4,13,21

%N Number of distinct prime factors of sigma_n(n).

%H Daniel Suteu, <a href="/A352420/b352420.txt">Table of n, a(n) for n = 1..120</a>

%F a(n) = omega(sigma_n(n)) = A001221(A023887(n)).

%e a(5) = 3; a(5) = omega(sigma_5(5)) = omega(1^5+5^5) = omega(3126) = 3.

%p A342420 := proc(n)

%p     A001221(A023887(n)) ; # reuses other codes

%p end proc:

%p seq(A342420(n),n=1..20) ; # _R. J. Mathar_, Apr 06 2022

%t Table[PrimeNu[DivisorSigma[n, n]], {n, 30}]

%o (PARI) a(n) = omega(sigma(n, n)); \\ _Daniel Suteu_, Mar 23 2022

%o (Python)

%o from sympy import primefactors, factorint

%o 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 Cf. A001221 (omega), A023887 (sigma_n(n)).

%Y Cf. A064165, A347718.

%K nonn

%O 1,3

%A _Wesley Ivan Hurt_, Mar 21 2022

%E a(67)-a(75) from _Daniel Suteu_, Mar 23 2022