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

1,8

Links

Table of n, a(n) for n=1..90.

Eric Weisstein's World of Mathematics, Greatest Prime Factor

Formula

a(n) = |{j < n : gpf(j) = gpf(n)}|.

a(n) = A078899(n) - 1.

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}]

Crossrefs

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

Sequence in context: A062135 A190182 A371788 * A068926 A276770 A258291

Adjacent sequences: A377727 A377728 A377729 * A377731 A377732 A377733

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 05 2024

Status

approved