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A351563
a(n) is the exponent of the second smallest prime factor of n, or 0 if n is a power of a prime.
2
0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 1, 1, 0, 3, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 0, 1, 2, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 0, 2, 1, 2, 0, 1, 0, 1, 1, 1, 0, 3
OFFSET
1,18
LINKS
FORMULA
a(n) = A067029(A028234(n)).
EXAMPLE
For n = 4 = 2^2 there is no second smallest prime factor as 4 is a power of prime, therefore a(4) = 0.
For n = 18 = 2^1 * 3^2, the exponent of the second smallest prime factor (3) is 2, therefore a(18) = 2.
MATHEMATICA
Array[If[Length[#] < 2, 0, #[[2, -1]]] &@ FactorInteger[#] &, 108] (* Michael De Vlieger, Apr 01 2022 *)
PROG
(PARI) A351563(n) = if(1>=omega(n), 0, (factor(n))[2, 2]);
CROSSREFS
Cf. A000961 (positions of zeros), A001221, A028234, A067029.
Cf. also A119288, A351567.
Sequence in context: A046675 A275949 A357924 * A362983 A352822 A090418
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 01 2022
STATUS
approved