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 A358250 Numbers whose square has a number of divisors coprime to 210. 2
 1, 32, 64, 243, 256, 512, 729, 2048, 3125, 6561, 7776, 15552, 15625, 16384, 16807, 19683, 23328, 32768, 46656, 62208, 100000, 117649, 124416, 161051, 177147, 186624, 200000, 209952, 262144, 371293, 373248, 390625, 419904, 497664, 500000, 537824, 629856, 759375 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 210 is the product of the smallest 4 primes. Numbers k such that gcd(d(k^2), 210) = 1, where d(k) is the number of divisors of k (A000005). Also numbers with no exponents = 1 mod 3, 2 mod 5, or 3 mod 7; also numbers whose square has a number of divisors coprime to 105. - Charles R Greathouse IV, Dec 08 2022 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..5000 FORMULA Sum_{n>=1} 1/a(n) = Product_{p prime} (Sum_{k=2..210, gcd(k-1,210)=1} p^(k/2))/(p^105-1) = 1.05981355805... . - Amiram Eldar, Dec 06 2022 MATHEMATICA With[{nn = 2^20}, Select[Union@ Flatten@ Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}], CoprimeQ[DivisorSigma[0, #^2], 210] &]] PROG (PARI) is(n, f=factor(n))=if(n<32, return(n==1)); my(t=f[, 2]%105, N=19200959813818273241621521446046); for(i=1, #t, if(bittest(N, t[i]), return(0))); 1 \\ Charles R Greathouse IV, Dec 08 2022 CROSSREFS Subsequence of A069492 and hence of A036967, A036966, and A001694. Subsequence of other sequences of numbers k such that gcd(d(k^2), m) = 1: A350014 (m=6), A354179 (m=30). Cf. A000005, A000290, A008364. Sequence in context: A069492 A076469 A256819 * A235057 A339358 A249116 Adjacent sequences: A358247 A358248 A358249 * A358251 A358252 A358253 KEYWORD nonn AUTHOR Michael De Vlieger, Dec 03 2022 STATUS approved

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Last modified August 7 14:20 EDT 2024. Contains 375013 sequences. (Running on oeis4.)