This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367974 #47 Dec 30 2023 23:38:39
%S A367974 1,25,1024,6272,1953125,4117715,15813251,213797679,346146025,
%T A367974 488281250,714592137,1719341824,3676531250,10510100501,10852734375,
%U A367974 11214315503,17241013443,25421511971
%N A367974 Numbers which contain the "Look and Say" description (cf. A045918) of all their prime factors, counted with multiplicity.
%C A367974 Overlapping of the "Look and Say" prime factor description strings is allowed. It is likely, although unproven, that 25 = 5*5 = "two 5's" = "25" is the only number that "perfectly" describes its own "Look and Say" factorization, i.e., there are no overlapping factor description strings, and all digits of the number are used in the factor description strings. It is unknown if the sequence is infinite.
%C A367974 There are many terms of the form 5^k, where k is 2, 9, 55, 62, 71, 82, 84, 86, 125, etc. - _Ivan N. Ianakiev_, Dec 07 2023
%C A367974 3262027661312 is a term. - _Martin Ehrenstein_, Dec 08 2023
%C A367974 10852734375 is a term. - _Michael S. Branicky_, Dec 08 2023
%C A367974 10510100501 is a term. - _Michael S. Branicky_, Dec 09 2023
%e A367974 1 is a term since it has no prime factors.
%e A367974 25 is a term as 25 = 5*5, i.e., two 5's being "25", which appears in 25.
%e A367974 1024 is a term as 1024 = 2^10, i.e., ten 2's being "102", which appears in 1024.
%e A367974 346146025 is a term as 346146025 = 5^2 * 61^4, i.e., two 5's and four 61's being "25" and "461", respectively, both of which appear in 346146025.
%e A367974 1719341824 is a term as 1719341824 = 2^8 * 719 * 9341, i.e., eight 2's and one 719 and one 9341 being "82", "1719" and "19341" respectively, all of which appear in 1719341824. Note that only the final digit 4 is not used in the string descriptions.
%t A367974 l[n_]:=ToString/@Reverse[Flatten[FactorInteger[n]]]; len[n_]:=Length[l[n]];
%t A367974 fQ[n_]:=AllTrue[Table[StringJoin[l[n][[i]],l[n][[i+1]]],{i,1,len[n],2}], StringPosition[ToString[n],#]!={}&]; Select[Range[6272],fQ[#]&] (* _Ivan N. Ianakiev_, Dec 07 2023 *)
%o A367974 (Python)
%o A367974 from sympy import factorint
%o A367974 def ok(n):
%o A367974 s = str(n)
%o A367974 return all(str(e)+str(p) in s for p, e in factorint(n).items())
%o A367974 print([k for k in range(10**5) if ok(k)]) # _Michael S. Branicky_, Dec 08 2023
%Y A367974 Cf. A045918, A005150, A027746.
%K A367974 nonn,base,more
%O A367974 1,2
%A A367974 _Scott R. Shannon_, Dec 07 2023
%E A367974 1 prepended by _Martin Ehrenstein_, Dec 08 2023
%E A367974 a(14)-a(16) from _Michael S. Branicky_, Dec 13 2023
%E A367974 a(17)-a(18) from _Michael S. Branicky_, Dec 27 2023