A377730 Number of integers less than n that have the same greatest prime factor as n.
0, 0, 0, 1, 0, 1, 0, 2, 2, 1, 0, 3, 0, 1, 2, 3, 0, 4, 0, 3, 2, 1, 0, 5, 4, 1, 6, 3, 0, 5, 0, 4, 2, 1, 4, 7, 0, 1, 2, 6, 0, 5, 0, 3, 7, 1, 0, 8, 6, 8, 2, 3, 0, 9, 4, 7, 2, 1, 0, 9, 0, 1, 8, 5, 4, 5, 0, 3, 2, 9, 0, 10, 0, 1, 10, 3, 6, 5, 0, 11, 11, 1, 0, 10, 4, 1, 2, 7, 0, 12
Offset: 1
Keywords
Links
- Eric Weisstein's World of Mathematics, Greatest Prime Factor
Programs
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Maple
R:= NULL: for n from 1 to 100 do p:= max(numtheory:-factorset(n)); if assigned(C[p]) then C[p]:= C[p]+1 else C[p]:= 0 fi; R:= R, C[p] od:R; # Robert Israel, Nov 07 2024
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Mathematica
Table[Length[Select[Range[n - 1], FactorInteger[#][[-1, 1]] == FactorInteger[n][[-1, 1]] &]], {n, 90}]
Formula
a(n) = |{j < n : gpf(j) = gpf(n)}|.
a(n) = A078899(n) - 1.