A332646 - OEIS

%I #12 Sep 08 2022 08:46:25

%S 1,4,9,25,49,64,121,169,289,361,529,729,841,961,1296,1369,1681,1849,

%T 2209,2809,3481,3721,4096,4489,5041,5329,6241,6889,7921,9409,10000,

%U 10201,10609,11449,11881,12769,15625,16129,17161,18769,19321,22201,22801,24649,26569

%N Numbers m with a divisor d such that d^tau(d) = m.

%C Possible values for function n^tau(n) (A062758).

%C Supersequence of A189991 (numbers with prime factorization p^4*q^4; d = pq), A001248 (numbers with prime factorization p^2; d = p), A030516 (numbers with prime factorization p^6; d = p^2) and A280076.

%e 64 is a term because 4^3 = 64; 4 divides 64; tau(4) = 3.

%t divPowerQ[n_] := AnyTrue[Divisors[n], #^DivisorSigma[0, #] == n &]; Select[Range[27000], divPowerQ] (* _Amiram Eldar_, Feb 18 2020 *)

%o (Magma) [n: n in [1..100000] | #[d: d in Divisors(n) | d^NumberOfDivisors(d) eq n] ge 1]

%o (PARI) isok(m) = fordiv(m, d, if (d^numdiv(d) == m, return (1))); \\ _Michel Marcus_, Feb 18 2020

%Y Cf. A000005, A001248, A030516, A062758, A189991, A280076.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Feb 18 2020