A365806 Numbers k such that A243071(k) is a square.

1, 2, 8, 27, 32, 45, 99, 108, 128, 135, 180, 369, 396, 432, 512, 540, 567, 675, 720, 855, 1287, 1476, 1584, 1728, 2048, 2160, 2205, 2268, 2673, 2700, 2880, 3420, 5148, 5445, 5904, 6336, 6912, 7803, 8073, 8192, 8640, 8820, 9072, 9477, 10125, 10647, 10692, 10800, 11520, 13680, 17325, 18513, 20592, 21780, 23616, 25344

Offset: 1

Author

Antti Karttunen, Oct 01 2023

Keywords

• nonn

Comments

Sequence A163511(n^2), n >= 0, sorted into ascending order.

Contains no squares after the initial 1. See A365808 for a proof.

Question: Are there any more odd cubes or odd powers after 1, 27, 35937 ?

Crossrefs

Cf. A000290, A004171 (subsequence), A010052, A163511, A243071, A365808.

Programs

PARI

A243071(n) = if(n<=2, n-1, my(f=factor(n), p, p2=1, res=0); for(i=1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p*p2*(2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); ((3<<#binary(res\2))-res-1)); \\ (Combining programs given in A156552 and A054429)
isA365806(n) = issquare(A243071(n));