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 A294110 Numbers with prime factorization of the form p_1^p_2*p_2^p_3*...p_(n-1)^p_n*p_n where p_(n-1) < p(n) and n > 1. 1
 24, 160, 896, 1215, 9720, 15309, 22528, 106496, 122472, 546875, 1948617, 2228224, 9961472, 15588936, 17500000, 20726199, 132890625, 165809592, 192937984, 537109375, 1063125000, 2195382771, 15569256448, 15869140625, 17187500000, 17563062168, 21750594173, 22082967873, 66571993088, 130517578125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All members of this sequence, by definition, only have primes and 1 as exponents of prime factors. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 EXAMPLE 24 is part of the sequence because its prime factorization is 2^3*3. 122472 is part of the sequence because its prime factorization is 2^3*3^7*7 10756480 is not part of the sequence because it prime factorization is 2^7*7^5*5. This does not follow the rule where each base in the chain must be greater than the previous (7<5 is not true). PROG (Python 3) def prime_factors(n):     factors = {}     i = 2     while n != 1:         while n % i == 0:             n /= i             if i in factors:                 factors[i] += 1             else:                 factors[i] = 1         i += 1     return factors def a(n):     i = 1     c = 0     while c < n:         i += 1         p = prime_factors(i)         if len(p) > 1 and list(p.keys())[1:]+[1] == list(p.values()):             c +=1     return i (PARI) is(n)=my(f=factor(n)); if(#f~<2, return(0)); for(i=2, #f~, if(f[i, 1]!=f[i-1, 2], return(0))); f[#f~, 2]==1 \\ Charles R Greathouse IV, Oct 22 2017 (PARI) get(q, N)=my(v, pq); if(N>>q == 0, return(if(N<1, [], [1]))); v=List([1]); forprime(p=2, min(sqrtnint(N, q), q-1), pq=p^q; u=pq*get(p, N\pq); for(i=1, #u, listput(v, u[i])); u=0); Set(v) list(lim)=my(v=List(), u, t); lim\=1; forprime(q=3, lambertw(log(2)*lim)\log(2), forprime(p=2, min(sqrtnint(lim, q), q-1), t=p^q*q; u=t*get(p, lim\t); for(i=1, #u, listput(v, u[i])); u=0)); Set(v) \\ Charles R Greathouse IV, Oct 22 2017 CROSSREFS Subsequence of A046099. Sequence in context: A231341 A186862 A305165 * A136380 A250323 A250142 Adjacent sequences:  A294107 A294108 A294109 * A294111 A294112 A294113 KEYWORD nonn AUTHOR Matthew McCaskill, Oct 22 2017 EXTENSIONS a(10)-a(30) from Charles R Greathouse IV, Oct 22 2017 Definition corrected by Jens Kruse Andersen, Oct 28 2017 STATUS approved

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Last modified November 29 09:18 EST 2021. Contains 349416 sequences. (Running on oeis4.)