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A372280 Composite numbers k such that the digits of k are in nondecreasing order while the digits of the concatenation of k's ascending order prime factors, with repetition, are in nonincreasing order.

%I A372280 #28 Apr 27 2024 08:58:34
%S A372280 4,8,9,16,22,25,27,33,44,49,55,77,88,99,125,128,155,256,279,1477,1555,
%T A372280 1688,1899,2799,3479,3577,14777,16888,18999,22599,36799,444577,455777,
%U A372280 1112447,1555555,2555555,2799999,3577777,3799999,45577777,124556677,155555555555,279999999999
%N A372280 Composite numbers k such that the digits of k are in nondecreasing order while the digits of the concatenation of k's ascending order prime factors, with repetition, are in nonincreasing order.
%C A372280 A number 155...555 will be a term if it has two prime factors 5 and 3111...111. Therefore 155555555555 and 1555555555555 are both terms. See A056704.
%C A372280 The next term is greater than 10^11.
%H A372280 Michael S. Branicky, <a href="/A372280/b372280.txt">Table of n, a(n) for n = 1..64</a> (all terms <= 20 digits)
%e A372280 444577 is a term as 444577 = 7 * 7 * 43 * 211, and 444577 has nondecreasing digits while its prime factor concatenation "7743211" has nonincreasing digits.
%o A372280 (Python)
%o A372280 from sympy import factorint, isprime
%o A372280 from itertools import count, islice, combinations_with_replacement as mc
%o A372280 def ni(s): return s == "".join(sorted(s, reverse=True))
%o A372280 def bgen(d):
%o A372280     yield from ("".join(m) for m in mc("0123456789", d) if m[0]!="0")
%o A372280 def agen(): # generator of terms
%o A372280     for d in count(1):
%o A372280         for s in bgen(d):
%o A372280             t = int(s)
%o A372280             if t < 4 or isprime(t): continue
%o A372280             if ni("".join(str(p)*e for p,e in factorint(t).items())):
%o A372280                 yield t
%o A372280 print(list(islice(agen(), 41))) # _Michael S. Branicky_, Apr 26 2024
%Y A372280 Cf. A372308, A372034, A056704, A372029, A372055, A027746, A372249.
%K A372280 nonn,base
%O A372280 1,1
%A A372280 _Scott R. Shannon_, Apr 25 2024
%E A372280 a(42)-a(43) from _Michael S. Branicky_, Apr 26 2024