A207359 Indices n, not squarefree, where A055231(n) = A055231(n-A055231(n)).

9, 45, 63, 99, 117, 153, 171, 207, 261, 279, 289, 315, 333, 369, 387, 423, 477, 495, 531, 549, 585, 603, 639, 657, 676, 693, 711, 747, 765, 801, 819, 855, 873, 909, 927, 963, 981, 1017, 1035, 1071, 1143, 1179, 1197, 1233, 1251, 1287, 1305, 1341, 1359, 1395

Offset: 1

Author

Michel Lagneau, Feb 17 2012

Keywords

• nonn

Comments

A055231(n) is the powerfree part of n. This sequence is infinite because all numbers of the form n = 9p, where p is a prime > 3, are in the sequence : A055231(9p) = p and A055231(9p - p) = A055231(8p) = p. The positive numbers of A055792 are also in the sequence because A055792(n) are squares and A055792(n)-1 are also squares.

Examples

			63 is in the sequence because A055231(63) = A055231(7*3^2) = 7, A055231(63 - 7) = A055231(56) = A055231(7*2^3) = 7.
		

Crossrefs

Cf. A055231, A140394.

Programs

Maple

isA013929 := proc(n)
    n>3 and not numtheory[issqrfree](n) ;
end proc:
isA207359 := proc(n)
    isA013929(n) and (A055231(n)- A055231(n- A055231(n))=0);
end proc:
for n from 1 to 5000 do
      if isA207359(n) then
          printf(`%d, `,n);
      end if;
end do: #  adapted from A140394.