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%I #8 Jun 07 2024 14:21:22
%S 1,68,547,2119,5817,13008,25412,45078,74409,116147,173379,249532,
%T 348375,474018,630922,823885,1058051,1338898,1672260,2064302,2521535,
%U 3050825,3659361,4354687,5144682,6037582,7041946,8166692,9421074,10814695,12357491,14059744,15932086,17985473
%N Position of 210^n among 7-smooth numbers A002473.
%C Also position of 210^(n+1) in A147571.
%t Table[
%t Sum[Floor@ Log[7, 210^n/(2^i*3^j*5^k)] + 1,
%t {i, 0, Log[2, 210^n]},
%t {j, 0, Log[3, 210^n/2^i]},
%t {k, 0, Log[5, 210^n/(2^i*3^j)]}],
%t {n, 0, 12}]
%o (Python)
%o import heapq
%o from itertools import islice
%o from sympy import primerange
%o def A372401gen(p=7): # generator for p-smooth terms
%o v, oldv, psmooth_primes, = 1, 0, list(primerange(1, p+1))
%o h = [(1, [0]*len(psmooth_primes))]
%o idx = {psmooth_primes[i]:i for i in range(len(psmooth_primes))}
%o loc = 0
%o while True:
%o v, e = heapq.heappop(h)
%o if v != oldv:
%o loc += 1
%o if len(set(e)) == 1:
%o yield loc
%o oldv = v
%o for p in psmooth_primes:
%o vp, ep = v*p, e[:]
%o ep[idx[p]] += 1
%o heapq.heappush(h, (v*p, ep))
%o print(list(islice(A372401gen(), 15))) # _Michael S. Branicky_, Jun 05 2024
%Y Cf. A002110, A002473, A022330, A147571, A202821, A372400, A372402.
%K nonn
%O 0,2
%A _Michael De Vlieger_, Jun 03 2024
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