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Smallest prime factors of numbers that are not prime powers.
+10
4
2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 5, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 5, 2, 3, 2, 2, 2, 3, 5, 2, 2, 3, 2, 2, 2, 3, 2, 7, 2, 2, 2, 2, 5, 2, 3, 2, 2, 7, 2, 3, 2, 5, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 5, 2, 3, 2, 7, 2, 2, 3, 2, 2, 3, 2, 2, 7, 2, 3, 2, 2, 2, 3, 2, 11, 2, 5, 2, 3, 2, 2, 2, 3, 2
FORMULA
a(n) > 2 iff n+1 and n+2 are prime powers ( A006549).
MATHEMATICA
s[n_] := Module[{f = FactorInteger[n]}, If[Length[f] > 1, f[[1, 1]], Nothing]]; Array[s, 200] (* Amiram Eldar, Oct 10 2024 *)
Largest prime factors of numbers that are not prime powers.
+10
4
3, 5, 3, 7, 5, 3, 5, 7, 11, 3, 13, 7, 5, 11, 17, 7, 3, 19, 13, 5, 7, 11, 5, 23, 3, 5, 17, 13, 3, 11, 7, 19, 29, 5, 31, 7, 13, 11, 17, 23, 7, 3, 37, 5, 19, 11, 13, 5, 41, 7, 17, 43, 29, 11, 5, 13, 23, 31, 47, 19, 3, 7, 11, 5, 17, 13, 7, 53, 3, 11, 37, 7, 19, 23, 29, 13, 59, 17, 5, 61
MATHEMATICA
s[n_] := Module[{f = FactorInteger[n]}, If[Length[f] > 1, f[[-1, 1]], Nothing]]; Array[s, 200] (* Amiram Eldar, Oct 10 2024 *)
Number of prime factors of numbers that are not prime powers (with multiplicity).
+10
4
2, 2, 3, 2, 2, 3, 3, 2, 2, 4, 2, 3, 3, 2, 2, 2, 4, 2, 2, 4, 3, 3, 3, 2, 5, 3, 2, 3, 4, 2, 4, 2, 2, 4, 2, 3, 2, 3, 3, 2, 3, 5, 2, 3, 3, 2, 3, 5, 2, 4, 2, 2, 2, 4, 4, 2, 3, 2, 2, 2, 6, 3, 3, 4, 3, 4, 3, 2, 5, 3, 2, 5, 3, 2, 3, 3, 2, 2, 5, 2, 2, 3, 4, 2, 3, 4, 2, 2, 4, 4, 3, 4, 2, 2, 2, 6, 2, 2, 3, 3, 4, 4, 3, 3, 2
MATHEMATICA
s[n_] := Module[{f = FactorInteger[n]}, If[Length[f] > 1, Total[f[[;; , 2]]], Nothing]]; Array[s, 200] (* Amiram Eldar, Oct 10 2024 *)
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