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A344473 Numbers of the form (q1^b1)(q2^b2)(q3^b3)(q4^b4)(q5^b5)... where q1=7, q2=13, q3=19, q4=31, q5=37, ... (A002476) and b1>=b2>=b3>=b4>=b5...

%I A344473 #11 May 20 2021 22:43:18
%S A344473 1,7,49,91,343,637,1729,2401,4459,8281,12103,16807,31213,53599,57967,
%T A344473 84721,117649,157339,218491,375193,405769,593047,753571,823543,
%U A344473 1101373,1529437,1983163,2626351,2840383,2989441,4151329,4877509,5274997,5764801,7709611
%N A344473 Numbers of the form (q1^b1)(q2^b2)(q3^b3)(q4^b4)(q5^b5)... where q1=7, q2=13, q3=19, q4=31, q5=37, ... (A002476) and b1>=b2>=b3>=b4>=b5...
%C A344473 A343771 is a subsequence.
%H A344473 Jianing Song, <a href="/A344473/b344473.txt">Table of n, a(n) for n = 1..10000</a>
%e A344473 12103 is a term since 12103 = 7^2 * 13 * 19.
%e A344473 22477 is not a term since 22477 = 7 * 13^2 * 19, the exponents are not nonincreasing.
%o A344473 (PARI) \\ following program for A054994
%o A344473 list_A344473(lim) =
%o A344473 {
%o A344473     my(u = [1], v = List(), w = v, pr, t = 1);
%o A344473     forprime(p = 7, ,
%o A344473         if (p % 3 > 1, next);
%o A344473         t *= p;
%o A344473         if (t > lim,
%o A344473             break);
%o A344473         listput(w, t)
%o A344473     );
%o A344473     for (i = 1, #w,
%o A344473         pr = 1;
%o A344473         for (e = 1, logint(lim\ = 1, w[i]),
%o A344473             pr *= w[i];
%o A344473             for (j = 1, #u,
%o A344473                 t = pr * u[j];
%o A344473                 if (t > lim,
%o A344473                     break);
%o A344473                 listput(v, t)
%o A344473             )
%o A344473         );
%o A344473         if (w[i] ^ 2 < lim, u = Set(concat(Vec(v), u)); v = List());
%o A344473     );
%o A344473     Set(concat(Vec(v), u));
%o A344473 }
%o A344473 list_A344473(100000)
%Y A344473 Cf. A002476, A343771, A054994.
%K A344473 nonn,easy
%O A344473 1,2
%A A344473 _Jianing Song_, May 20 2021