A207360 Numbers n, not squarefree, satisfying A055231(n) = A055231(n + A055231(n)).

8, 40, 56, 88, 104, 136, 152, 184, 232, 248, 280, 288, 296, 328, 344, 376, 424, 440, 472, 488, 520, 536, 568, 584, 616, 632, 664, 675, 680, 712, 728, 760, 776, 808, 824, 856, 872, 904, 920, 952, 1016, 1048, 1064, 1096, 1112, 1144, 1160, 1192, 1208, 1240, 1256

Offset

1,1

Comments

A055231(n) is the powerfree part of n.

This sequence is infinite because the numbers of the form n = 8p, where p is prime, are in the sequence : A055231(8p) = p and A055231(8p + p) = A055231(9p) = p.

The numbers such that n and n+1 are a pair of consecutive powerful numbers (the again infinite A060355) are also in the sequence because A055231 (A060355(n)) = A055231(A060355 (n+1)) = 1.

Links

Table of n, a(n) for n=1..51.

Example

136 is in the sequence because A055231(136) = A055231(17*2^3) = 17, A055231(136 + 17) = A055231(153) = A055231(17*3^2) = 17.

Maple

isA013929 := proc(n)
        n>3 and not numtheory[issqrfree](n) ;
end proc:
isA207360 := proc(n)
       isA013929(n)  and (A055231(n)- A055231(n+ A055231(n))=0);
end proc:
for n from 1 to 5000 do
        if isA207360(n) then
            printf(`%d, `, n);
        end if;
end do: # (adapted from A140394).

Mathematica

rad[n_] := Times @@ FactorInteger[n][[All, 1]];
A055231[n_] := Denominator[n/rad[n]^2];
Select[Range[2000], !SquareFreeQ[#] && A055231[#] == A055231[# + A055231[#]]&] (* Jean-François Alcover, Jun 18 2024 *)

Prog

(PARI) isA013929(n)={
    (n>3) && !issquarefree(n)
}
isA207360(n)={
    isA013929(n) && ( A055231(n)-A055231(n+A055231(n)) ==0)
}
{ for(n=1, 1300, if(isA207360(n), print1(n" ") ) ; ) ;
} /* R. J. Mathar, Mar 12 2012 */

Crossrefs

Cf. A055231, A060355, A140394.

Sequence in context: A154425 A120931 A213345 * A226904 A305075 A069083

Adjacent sequences: A207357 A207358 A207359 * A207361 A207362 A207363

Keyword

nonn

Author

Michel Lagneau, Feb 17 2012

Status

approved