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A376833
Second smallest prime factor of numbers m that are both squarefree and composite.
1
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, 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, 47, 71, 13, 29, 73, 7, 31, 79, 53, 23, 5, 83, 5, 3, 59, 89, 7, 61, 37, 3
OFFSET
1,1
LINKS
Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^20.
FORMULA
a(n) = A119288(A120944(n)).
For even squarefree semiprime A120944(n) = 2*p with odd prime p, a(n) = p sets a record in this sequence.
EXAMPLE
Let b(n) = A120944(n).
a(1) = 3 since b(1) = 6, and 3 is the second smallest prime factor.
a(2) = 5 since b(2) = 10, and 5 is the second smallest prime factor.
Table showing select values of a(n):
n b(n) a(n)
-----------------------
1 6 = 2*3 3
2 10 = 2*5 5
3 14 = 2*7 7
4 15 = 3*5 5
5 21 = 3*7 7
6 22 = 2*11 11
7 26 = 2*13 13
8 30 = 2*3*5 3
14 42 = 2*3*7 3
22 66 = 2*3*11 3
24 70 = 2*5*7 5
82 210 = 2*3*5*7 3
MATHEMATICA
Map[FactorInteger[#][[2, 1]] &, Select[Range[250], And[SquareFreeQ[#], CompositeQ[#]] &]]
PROG
(Python)
from math import isqrt
from sympy import primepi, mobius, primefactors
def A376833(n):
def f(x): return n+1+primepi(x)+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
m, k = n+1, f(n+1)
while m != k:
m, k = k, f(k)
return primefactors(m)[1] # Chai Wah Wu, Oct 06 2024
CROSSREFS
Sequence in context: A141710 A279399 A321784 * A225889 A070647 A070949
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Oct 05 2024
STATUS
approved