A137257 -id:A137257 - cp's OEIS frontend

A368715 Numbers that are not coprime to the maximal exponent in their prime factorization.

4, 12, 16, 18, 20, 24, 27, 28, 36, 44, 48, 50, 52, 54, 60, 64, 68, 72, 76, 80, 84, 90, 92, 98, 100, 108, 112, 116, 120, 124, 126, 132, 135, 140, 144, 148, 150, 156, 160, 162, 164, 168, 172, 176, 180, 188, 189, 192, 196, 198, 204, 208, 212, 216, 220, 228, 234, 236, 240, 242, 244

Offset: 1

Amiram Eldar, Jan 04 2024

Subsequence of A137257 and first differs from it at n = 51.
Numbers k such that gcd(k, A051903(k)) > 1.
Includes all the nonsquarefree terms of A336064.
The asymptotic density of this sequence is 1 - 1/zeta(2) - Sum_{k>=2} (1/(f(k+1, k) * zeta(k+1)) - 1/(f(k, k) * zeta(k))) = 0.24998449199080279703..., where f(e, m) = Product_{primes p|m} ((1-1/p^e)/(1-1/p)).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A051903.
Subsequence of A013929 and A137257.
Similar sequences: A060476, A074661, A096432, A336064, A368714.

Select[Range[210], !CoprimeQ[#, Max[FactorInteger[#][[;;, 2]]]] &]

lista(kmax) = for(k = 2, kmax, if(gcd(k, vecmax(factor(k)[,2])) > 1, print1(k, ", ")));

A144976 Nonsquarefree numbers k such that k is divisible by the maximal exponent in the prime factorization of k.

Original entry on oeis.org

4, 12, 16, 18, 20, 24, 27, 28, 36, 44, 48, 50, 52, 54, 60, 68, 72, 76, 80, 84, 90, 92, 98, 100, 108, 112, 116, 120, 124, 126, 132, 135, 140, 144, 148, 150, 156, 160, 164, 168, 172, 176, 180, 188, 189, 192, 196, 198, 204, 208, 212, 216, 220, 228, 234, 236, 240, 242, 244, 252, 256, 260, 264, 268, 270, 272

Offset: 1

Giovanni Teofilatto, Sep 28 2008

nonn

The asymptotic density of this sequence is A336065 - A059956 = 0.24103009315... . - Amiram Eldar, Jan 05 2024

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Intersection of A013929 and A336064.

Cf. A059956, A137257, A336065.

A051903 := proc(n) local a,ifs,p,e; a := 1 ; max( seq(op(2,p),p=ifactors(n)[2]) ); end: isA013929 := proc(n) RETURN( not isprime(n) and A051903(n) > 1 ) ; end: isA144976 := proc(n) RETURN( isA013929(n) and (n mod A051903(n)) = 0 ); end: for n from 4 to 400 do if isA144976(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Oct 24 2008

Select[Range[300],!SquareFreeQ[#]&&Divisible[#,Max[FactorInteger[#][[All,2]]]]&] (* Harvey P. Dale, Jul 01 2017 *)

is(n) = {my(e = factor(n)[, 2], emax); if(n == 1, 0, emax = vecmax(e); emax > 1 && !(n % emax));} \\ Amiram Eldar, Jan 05 2024

{A013929(i): A051903(A013929(i)) | A013929(i)}. - R. J. Mathar, Oct 24 2008

Adapted definition, inserted 18, 20 and extended. - R. J. Mathar, Oct 24 2008

cp's OEIS Frontend

A368715 Numbers that are not coprime to the maximal exponent in their prime factorization.

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