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

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

1,1

Comments

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

Links

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

Formula

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

Maple

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

Mathematica

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

Prog

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

Crossrefs

Intersection of A013929 and A336064.

Cf. A059956, A137257, A336065.

Sequence in context: A157849 A137257 A368715 * A119622 A367909 A280892

Adjacent sequences: A144973 A144974 A144975 * A144977 A144978 A144979

Keyword

nonn

Author

Giovanni Teofilatto, Sep 28 2008

Extensions

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

Status

approved