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%I #29 Sep 08 2022 08:46:24
%S 1,3,18,6,648,20,2916,30,288,304,82944,60,36864,832,16200,168,
%T 5509980288,612,31719424,432,23328,44032,247669456896,420,9487368,
%U 258048,14112,2496,31581162962944,4176,26843545600,840,4064256,4390912,42693156,1980,151801324109824
%N a(n) = the smallest number m such that gcd(tau(m), sigma(m)) = n where tau(k) = the number of the divisors of k (A000005) and sigma(k) = the sum of the divisors of k (A000203).
%C a(n) = the smallest number m such that A009205(m) = n.
%C a(p) = q^(c*p-1) * k for p prime, where q is some prime, c and k are positive integers. - _David A. Corneth_, Mar 07 2019
%e For n=3; a(3) = 18 because gcd(tau(18), sigma(18)) = gcd (6, 39) = 3 and 18 is the smallest.
%t Array[Block[{m = 1}, While[GCD @@ DivisorSigma[{0, 1}, m] != #, m++]; m] &, 16] (* _Michael De Vlieger_, Mar 24 2019 *)
%o (Magma) [Min([n: n in[1..10^5] | GCD(NumberOfDivisors(n), SumOfDivisors(n)) eq k]): k in [1..16]]
%o (PARI) A324554search_and_print(searchlimit) = { my(m = Map(), k); for(n=1,searchlimit,k=gcd(sigma(n),numdiv(n)); if(!mapisdefined(m,k), mapput(m,k,n))); for(k=1, oo, if(!mapisdefined(m,k), break, print1(mapget(m,k), ", "))); }; \\ _Antti Karttunen_, Mar 06 2019
%Y Cf. A000005, A007955, A009205.
%Y Cf. also A324553, A324555.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Mar 05 2019
%E a(17)-a(37) from _Jon E. Schoenfield_, Mar 06 2019
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