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A306044
Powers of 2, 3 and 5.
5
1, 2, 3, 4, 5, 8, 9, 16, 25, 27, 32, 64, 81, 125, 128, 243, 256, 512, 625, 729, 1024, 2048, 2187, 3125, 4096, 6561, 8192, 15625, 16384, 19683, 32768, 59049, 65536, 78125, 131072, 177147, 262144, 390625, 524288, 531441, 1048576, 1594323, 1953125, 2097152, 4194304, 4782969, 8388608
OFFSET
1,2
COMMENTS
Union of A000079, A000244 and A000351.
LINKS
FORMULA
Sum_{n>=1} 1/a(n) = 11/4. - Amiram Eldar, Dec 10 2022
MAPLE
N:= 10^7: # for terms <= N
sort(convert(`union`(seq({seq(b^i, i=0..ilog[b](N))}, b=[2, 3, 5])), list)); # Robert Israel, Nov 18 2022
MATHEMATICA
Union[2^Range[0, Log2[5^10]], 3^Range[Log[3, 5^10]], 5^Range[10]]
PROG
(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
(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).
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Jun 18 2018
STATUS
approved