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...

1, 7, 49, 91, 343, 637, 1729, 2401, 4459, 8281, 12103, 16807, 31213, 53599, 57967, 84721, 117649, 157339, 218491, 375193, 405769, 593047, 753571, 823543, 1101373, 1529437, 1983163, 2626351, 2840383, 2989441, 4151329, 4877509, 5274997, 5764801, 7709611

Offset: 1

Author

Jianing Song, May 20 2021

Keywords

• nonn
• easy

Comments

A343771 is a subsequence.

Examples

			12103 is a term since 12103 = 7^2 * 13 * 19.
22477 is not a term since 22477 = 7 * 13^2 * 19, the exponents are not nonincreasing.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002476, A343771, A054994.

Programs

PARI

\\ following program for A054994
list_A344473(lim) =
{
    my(u = [1], v = List(), w = v, pr, t = 1);
    forprime(p = 7, ,
        if (p % 3 > 1, next);
        t *= p;
        if (t > lim,
            break);
        listput(w, t)
    );
    for (i = 1, #w,
        pr = 1;
        for (e = 1, logint(lim\ = 1, w[i]),
            pr *= w[i];
            for (j = 1, #u,
                t = pr * u[j];
                if (t > lim,
                    break);
                listput(v, t)
            )
        );
        if (w[i] ^ 2 < lim, u = Set(concat(Vec(v), u)); v = List());
    );
    Set(concat(Vec(v), u));
}
list_A344473(100000)