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A207360 Numbers n, not squarefree, satisfying A055231(n) = A055231(n + A055231(n)). 0
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 (list; graph; refs; listen; history; text; internal format)
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).

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

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Last modified January 18 04:46 EST 2019. Contains 319269 sequences. (Running on oeis4.)