A391841 Positive integers k with exactly sqrt(tau(k)) square divisors.

1, 8, 27, 125, 216, 343, 384, 640, 896, 1000, 1331, 1408, 1440, 1664, 2016, 2176, 2197, 2400, 2432, 2744, 2944, 3168, 3375, 3712, 3744, 3968, 4374, 4704, 4736, 4860, 4896, 4913, 5248, 5472, 5504, 5600, 6016, 6624, 6784, 6804, 6859, 7552, 7808, 7840, 8352, 8576

Offset

1,2

Comments

Numbers k for which A046951(k)^2 = A000005(k).

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Example

216 is a term because 216 has sqrt(tau(216)) = sqrt(16) = 4 square divisors (1, 4, 9, 36).

Maple

A391841 := proc(n) local d, k; option remember; if n = 1 then 1; else for k from A391841(n - 1) + 1 do d := NumberTheory:-Divisors(k); if nops(select(issqr, d))^2 = nops(d) then return k; end if; end do; end if; end proc: seq(A391841(n), n = 1 .. 46);

Prog

(PARI) isok(k) = my(f=factor(k)); sumdiv(f, i, issquare(i))^2 == numdiv(f); \\ Michel Marcus, Dec 30 2025

Crossrefs

Cf. A000005, A036436, A046951.

Sequence in context: A183316 A045971 A176509 * A179125 A030160 A030162

Adjacent sequences: A391838 A391839 A391840 * A391842 A391843 A391844

Keyword

nonn

Author

Felix Huber, Dec 30 2025

Status

approved