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

Author

Ilya Gutkovskiy, Nov 05 2024

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Greatest Prime Factor

Crossrefs

Cf. A006530, A047983, A078899, A334655, A335097, A377734.

Programs

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

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.