This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332646 #16 Mar 17 2025 15:48:23 %S A332646 1,4,9,25,49,64,121,169,289,361,529,729,841,961,1296,1369,1681,1849, %T A332646 2209,2809,3481,3721,4096,4489,5041,5329,6241,6889,7921,9409,10000, %U A332646 10201,10609,11449,11881,12769,15625,16129,17161,18769,19321,22201,22801,24649,26569 %N A332646 Numbers m with a divisor d such that d^tau(d) = m. %C A332646 Possible values for function n^tau(n) (A062758). %C A332646 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 A332646 64 is a term because 4^3 = 64; 4 divides 64; tau(4) = 3. %t A332646 divPowerQ[n_] := AnyTrue[Divisors[n], #^DivisorSigma[0, #] == n &]; Select[Range[27000], divPowerQ] (* _Amiram Eldar_, Feb 18 2020 *) %o A332646 (Magma) [n: n in [1..100000] | #[d: d in Divisors(n) | d^NumberOfDivisors(d) eq n] ge 1]; %o A332646 (PARI) isok(m) = fordiv(m, d, if (d^numdiv(d) == m, return (1))); \\ _Michel Marcus_, Feb 18 2020 %Y A332646 Cf. A000005, A001248, A030516, A062758, A189991, A280076. %K A332646 nonn %O A332646 1,2 %A A332646 _Jaroslav Krizek_, Feb 18 2020