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 A113877 Semiprimes to semiprime powers. 9
 256, 1296, 4096, 6561, 10000, 38416, 46656, 50625, 194481, 234256, 262144, 390625, 456976, 531441, 1000000, 1048576, 1185921, 1336336, 1500625, 2085136, 2313441, 4477456, 5764801, 6765201, 7529536, 9150625, 10077696, 10556001, 11316496, 11390625, 14776336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is the semiprime analog of A053810. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 FORMULA {a(n)} = {a^b where a and b are elements of A001358}. {a(n)} = {(p*q)^(r*s) = (p^(r*s))*(q^r*s) for distinct primes p, q, r, s} UNION {(p*q)^(p*r) = (p^(p*r))*(q^(p*r)) for distinct primes p, q, r} UNION {(p*q)^(r*r) = (p^(r^2))*(q^(r^2)) for distinct primes p, q, r} UNION {(p*q)^(p*q)= (p^(p*q))*(q^(p*q)) for distinct primes p, q} UNION {(p^2)^(p^2) = p^(2*(p^2)) for prime p}. a(n) ~ (n log n/log log n)^4. - Charles R Greathouse IV, Jun 05 2013 EXAMPLE a(1) = 256 = 4^4 = semiprime(1)^semiprime(1). a(2) = 1296 = 6^4 = semiprime(2)^semiprime(1). a(3) = 4096 = 4^6 = semiprime(1)^semiprime(2). a(4) = 6561 = 9^4 = semiprime(3)^semiprime(1). a(5) = 10000 = 10^4. MATHEMATICA lim = 10^8; s = Select[Range[lim^(1/4)], Total[Transpose[FactorInteger[#]][[2]]] == 2 &]; t = {}; j = 1; While[b = s[[j]]; i = 1; While[a = s[[i]]; e = a^b; If[e <= lim, AppendTo[t, e]]; e < lim && i < Length[s], i++]; i > 1, j++]; t = Union[t] (* T. D. Noe, Jun 05 2013 *) PROG (PARI) is(n)=my(b, e=ispower(n, , &b), o); if(e==0, return(0)); o=bigomega(e); (o==2 && bigomega(b)==2) || (e%2==0 && o==3 && isprime(b)) \\ Charles R Greathouse IV, Jun 05 2013 (PARI) list(lim)=my(v=List()); for(e=4, log(lim\=1+.5)\log(4), if(bigomega(e)!=2, next); for(b=4, (lim+.5)^(1/e), if(bigomega(b)==2, listput(v, b^e)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jun 05 2013 CROSSREFS Cf. A001358, A113854, A053810. Sequence in context: A237952 A237235 A129539 * A237398 A237392 A205097 Adjacent sequences: A113874 A113875 A113876 * A113878 A113879 A113880 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Jan 27 2006 EXTENSIONS Terms corrected by Charles R Greathouse IV, Jun 05 2013 STATUS approved

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Last modified June 23 16:55 EDT 2024. Contains 373653 sequences. (Running on oeis4.)