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%I #20 Nov 04 2023 12:26:45
%S 1,8,27,32,64,125,216,243,256,343,512,729,864,1000,1331,1728,1944,
%T 2048,2197,2744,3125,3375,4000,4913,5832,6561,6859,6912,7776,8000,
%U 9261,10648,10976,12167,13824,15552,15625,16384,16807,17576,19683,21952,23328,24389,25000
%N Numbers whose square has a number of divisors that is coprime to 30.
%C Numbers k such that gcd(d(k^2), 30) = 1, where d(k) is the number of divisors of k (A000005).
%H Michael De Vlieger, <a href="/A354179/b354179.txt">Table of n, a(n) for n = 1..10000</a> (first 1709 terms from Amiram Eldar)
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F a(n) = sqrt(A354178(n)).
%F Sum_{n>=1} 1/a(n) = Product_{p prime} (p + p^4 + p^6 + p^7 + p^9 + p^10 + p^12 + p^15)/(p^15 - 1) = 1.2449394393...
%e 8 is a term since A000005(8^2) = 7 and gcd(7, 30) = 1.
%t Select[Range[25000], CoprimeQ[DivisorSigma[0, #^2], 30] &]
%o (PARI) isok(m) = gcd(numdiv(m^2), 30) == 1; \\ _Michel Marcus_, May 19 2022
%Y Cf. A000005, A354178.
%Y Subsequence of A350014.
%K nonn
%O 1,2
%A _Amiram Eldar_, May 18 2022
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