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%I #41 Dec 10 2022 10:46:40
%S 1,2,3,4,5,8,9,16,25,27,32,64,81,125,128,243,256,512,625,729,1024,
%T 2048,2187,3125,4096,6561,8192,15625,16384,19683,32768,59049,65536,
%U 78125,131072,177147,262144,390625,524288,531441,1048576,1594323,1953125,2097152,4194304,4782969,8388608
%N Powers of 2, 3 and 5.
%C Union of A000079, A000244 and A000351.
%H Michel Marcus, <a href="/A306044/b306044.txt">Table of n, a(n) for n = 1..1370</a>
%F Sum_{n>=1} 1/a(n) = 11/4. - _Amiram Eldar_, Dec 10 2022
%p N:= 10^7: # for terms <= N
%p sort(convert(`union`(seq({seq(b^i,i=0..ilog[b](N))},b=[2,3,5])),list)); # _Robert Israel_, Nov 18 2022
%t Union[2^Range[0, Log2[5^10]], 3^Range[Log[3, 5^10]], 5^Range[10]]
%o (PARI) setunion(setunion(vector(logint(N=10^6,5)+1,k,5^(k-1)), vector(logint(N,3),k,3^k)), vector(logint(N,2),k,2^k)) \\ _M. F. Hasler_, Jun 24 2018
%o (PARI) a(n)= my(f=[2,3,5],q=sum(k=1,#f,1/log(f[k]))); for(i=1,#f, my(p=logint(exp(n/q),f[i]),d=0,j=0,m=0); while(j<n, m=f[i]^(p+d); j=1+sum(k=1,#f,logint(m,f[k])); if(j==n, return(m)); d++)) \\ _Ruud H.G. van Tol_, Nov 16 2022 (with the help of the pari-users mailing list) Observation: with f=primes(P), d <= logint(P,2).
%Y Cf. A000079, A000244, A000351, A006899.
%Y Cf. A226722, A226723, A226724.
%K nonn
%O 1,2
%A _Zak Seidov_, Jun 18 2018
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