cp's OEIS Frontend

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.

A358250 Numbers whose square has a number of divisors coprime to 210.

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%I A358250 #14 Dec 08 2022 09:55:02
%S A358250 1,32,64,243,256,512,729,2048,3125,6561,7776,15552,15625,16384,16807,
%T A358250 19683,23328,32768,46656,62208,100000,117649,124416,161051,177147,
%U A358250 186624,200000,209952,262144,371293,373248,390625,419904,497664,500000,537824,629856,759375
%N A358250 Numbers whose square has a number of divisors coprime to 210.
%C A358250 210 is the product of the smallest 4 primes.
%C A358250 Numbers k such that gcd(d(k^2), 210) = 1, where d(k) is the number of divisors of k (A000005).
%C A358250 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
%H A358250 Michael De Vlieger, <a href="/A358250/b358250.txt">Table of n, a(n) for n = 1..5000</a>
%F A358250 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
%t A358250 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] &]]
%o A358250 (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
%Y A358250 Subsequence of A069492 and hence of A036967, A036966, and A001694.
%Y A358250 Subsequence of other sequences of numbers k such that gcd(d(k^2), m) = 1: A350014 (m=6), A354179 (m=30).
%Y A358250 Cf. A000005, A000290, A008364.
%K A358250 nonn
%O A358250 1,2
%A A358250 _Michael De Vlieger_, Dec 03 2022