A391841 - OEIS

%I #7 Jan 04 2026 20:49:38

%S 1,8,27,125,216,343,384,640,896,1000,1331,1408,1440,1664,2016,2176,

%T 2197,2400,2432,2744,2944,3168,3375,3712,3744,3968,4374,4704,4736,

%U 4860,4896,4913,5248,5472,5504,5600,6016,6624,6784,6804,6859,7552,7808,7840,8352,8576

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

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

%H Felix Huber, <a href="/A391841/b391841.txt">Table of n, a(n) for n = 1..10000</a>

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

%p 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);

%o (PARI) isok(k) = my(f=factor(k)); sumdiv(f, i, issquare(i))^2 == numdiv(f); \\ _Michel Marcus_, Dec 30 2025

%Y Cf. A000005, A036436, A046951.

%K nonn

%O 1,2

%A _Felix Huber_, Dec 30 2025