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%I #36 Feb 23 2026 10:33:43
%S 1,2,3,4,5,6,7,8,9,14,15,20,24,27,35,48,49,63,80,125,224,2400,4374,
%T 250000,78121827,205885750000000,2251783932057135,
%U 363797880709171295166015625,37252879910233655318543787489,639471113830161648869830843378434048,386856165263818792142417337638583138065421
%N 7-smooth numbers k such that k / (next 7-smooth number after k) reaches a record large value.
%H Zhicheng Wei, <a href="/A392635/b392635.txt">Table of n, a(n) for n = 1..35</a>
%e From _Michael De Vlieger_, Feb 20 2026: (Start)
%e Let s = A002473 and let facs(x) represent the standard form prime decomposition of x.
%e Table of n, a(n) = s(i) for select n:
%e n i a(n) facs(a(n)) facs(s(i+1))
%e --------------------------------------------------------
%e 1 1 1 1 2
%e 2 2 2 2 3
%e 3 3 3 3 2^2
%e 4 4 4 2^2 5
%e 5 5 5 5 2 * 3
%e 12 16 20 2^2 * 5 3 * 7
%e 13 18 24 2^3 * 3 5^2
%e 14 20 27 3^3 2^2 * 7
%e 21 70 224 2^5 * 7 3^2 * 5^2
%e 22 201 2400 2^5 * 3 * 5^2 7^4
%e 28 289773 5^38 2^42 * 3^15 * 7^8
%e 32 7313064 2^193 * 3^6 5^5 * 7^68 (End)
%t (* First, load "regs" function from "Fast Mathematica programs" at A369609, then: *) Numerator@ Union@ FoldList[Max, Divide @@@ Partition[regs[210, 2^150], 2, 1] ] (* _Michael De Vlieger_, Feb 19 2026 *)
%o (Python) # uses A002473gen() in A002473
%o from itertools import islice
%o from fractions import Fraction
%o def agen():
%o g = A002473gen(); k = next(g); record = 0
%o while True:
%o nextk = next(g); f = Fraction(k, nextk)
%o if f > record: yield k; record = f
%o k = nextk
%o print(list(islice(agen(), 30)))
%Y Cf. A002473, A085153. Starts with A085153.
%K nonn
%O 1,2
%A _Zhicheng Wei_, Feb 19 2026