A047983 -id:A047983 - cp's OEIS frontend

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

Ilya Gutkovskiy, Nov 05 2024

nonn

Eric Weisstein's World of Mathematics, Greatest Prime Factor

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

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

Table[Length[Select[Range[n - 1], FactorInteger[#][[-1, 1]] == FactorInteger[n][[-1, 1]] &]], {n, 90}]

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

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

A338504 Number of integers less than n with the same sum of proper divisors as n.

Original entry on oeis.org

0, 0, 1, 0, 2, 0, 3, 0, 0, 0, 4, 0, 5, 0, 0, 0, 6, 0, 7, 0, 0, 0, 8, 0, 1, 1, 0, 0, 9, 0, 10, 0, 1, 0, 1, 0, 11, 1, 0, 0, 12, 0, 13, 0, 0, 0, 14, 0, 1, 0, 1, 0, 15, 0, 1, 0, 0, 0, 16, 0, 17, 0, 0, 0, 0, 0, 18, 0, 0, 0, 19, 0, 20, 1, 0, 1, 1, 0, 21, 0, 2, 0, 22, 0, 1, 1, 1, 0, 23, 0, 2

Offset: 1

Ilya Gutkovskiy, Oct 31 2020

nonn

			a(5) = 2 because A001065(5) = 1 and also A001065(2) = A001065(3) = 1.

Cf. A001065, A047983, A263025.

Table[Length[Select[Range[n - 1], DivisorSigma[1, #] - # == DivisorSigma[1, n] - n &]], {n, 91}]

a(n)={my(t=sigma(n)-n); sum(k=1, n-1, sigma(k)-k==t)} \\ Andrew Howroyd, Oct 31 2020

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

cp's OEIS Frontend

A377730 Number of integers less than n that have the same greatest prime factor as n.

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