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%I #14 Oct 07 2024 00:43:31
%S 3,5,7,5,7,11,13,3,11,17,7,19,13,3,23,17,11,19,29,31,13,3,23,5,37,11,
%T 3,41,17,43,29,13,31,47,19,3,5,53,5,37,3,23,59,17,61,41,43,5,19,67,3,
%U 47,71,13,29,73,7,31,79,53,23,5,83,5,3,59,89,7,61,37,3
%N Second smallest prime factor of numbers m that are both squarefree and composite.
%H Michael De Vlieger, <a href="/A376833/b376833.txt">Table of n, a(n) for n = 1..10000</a>
%H Michael De Vlieger, <a href="/A376833/a376833.png">Log log scatterplot of a(n)</a>, n = 1..2^20.
%F a(n) = A119288(A120944(n)).
%F For even squarefree semiprime A120944(n) = 2*p with odd prime p, a(n) = p sets a record in this sequence.
%e Let b(n) = A120944(n).
%e a(1) = 3 since b(1) = 6, and 3 is the second smallest prime factor.
%e a(2) = 5 since b(2) = 10, and 5 is the second smallest prime factor.
%e Table showing select values of a(n):
%e n b(n) a(n)
%e -----------------------
%e 1 6 = 2*3 3
%e 2 10 = 2*5 5
%e 3 14 = 2*7 7
%e 4 15 = 3*5 5
%e 5 21 = 3*7 7
%e 6 22 = 2*11 11
%e 7 26 = 2*13 13
%e 8 30 = 2*3*5 3
%e 14 42 = 2*3*7 3
%e 22 66 = 2*3*11 3
%e 24 70 = 2*5*7 5
%e 82 210 = 2*3*5*7 3
%t Map[FactorInteger[#][[2, 1]] &, Select[Range[250], And[SquareFreeQ[#], CompositeQ[#]] &]]
%o (Python)
%o from math import isqrt
%o from sympy import primepi, mobius, primefactors
%o def A376833(n):
%o def f(x): return n+1+primepi(x)+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
%o m, k = n+1, f(n+1)
%o while m != k:
%o m, k = k, f(k)
%o return primefactors(m)[1] # _Chai Wah Wu_, Oct 06 2024
%Y Cf. A119288, A120944.
%K nonn,easy
%O 1,1
%A _Michael De Vlieger_, Oct 05 2024