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A075047 Numbers k whose prime factorization contains the same digits as k.

%I A075047 #53 Feb 20 2024 07:01:31
%S A075047 25,121,471663,931225,4473225,6953931,7301441,10713728,13246317,
%T A075047 17332133,19367424,34706961,36310761,54363717,68714219,73553125,
%U A075047 73641071,74390183,93478133,102712448,102941361,109502361,113162997,115521875,120934784,134179011,134381673,134472875,135478125
%N A075047 Numbers k whose prime factorization contains the same digits as k.
%C A075047 From _Robert G. Wilson v_, Jun 06 2014, updated Jun 10 2014: (Start)
%C A075047 The number of terms < 10^n: 0, 1, 2, 2, 2, 4, 7, 19, 71, 289, ..., .
%C A075047 There are only two terms which have just one prime factor (excluding multiplicity), i.e., 25 and 121. By index, they are 1 and 2.
%C A075047 The least term with just two prime factors is 471663. By index, they are 3, 4, 6, 7, 8, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 25, ..., .
%C A075047 The least term with just three prime factors is 4473225. By index, they are 5, 9, 10, 11, 23, 24, 26, 28, 29, 30, 32, 36, 38, 39, 44, 46, 47, 66, ..., .
%C A075047 The least term with just four prime factors is 1713131455. By index, they are 110, 115, 251, ..., .
%C A075047 The least term with k prime factors (including multiplicity), or 0 if impossible or -1 not yet found, are 0, 25, 0, 931225, 7301441, 73553125, 471663, 4473225, 141294375, 251317472, 134179011, 1931229184, -1, 19367424, ..., .
%C A075047 So far ( < 10000000000) the count of digits 1,2,...,9,0 is {520, 271, 388, 254, 216, 211, 371, 172, 262, 117}.
%C A075047 (End)
%H A075047 Giovanni Resta, <a href="/A075047/b075047.txt">Table of n, a(n) for n = 1..1000</a> (first 311 terms from Robert G. Wilson v)
%e A075047 25 = 5^2 and 121 = 11^2 are terms.
%e A075047 The term 1971753273 -> 1,9,7,1,7,5,3,2,7,3 -> 1,1,2,3,3,5,7,7,7,9 is in the sequence because its factorization is 3^7*7^1*37^1*59^2 -> 3,7,7,1,3,7,1,5,9,2 -> 1,1,2,3,3,5,7,7,7,9 and this coincides with the digits of the term itself. - _Robert G. Wilson v_, Jun 06 2014
%t A075047 fQ[n_] := Sort@ IntegerDigits@ n == Sort@ Flatten@ IntegerDigits@ FactorInteger@ n; k = 1; lst = {}; While[k < 100000001, If[ fQ@ k, AppendTo[lst, k]; Print@ k]; k++]; lst (* _Robert G. Wilson v_, Jun 05 2014 *)
%o A075047 (PARI) isok(n, b=10) = {f = factor(n); v = []; for (i=1, #f~, v = concat(v, digits(f[i,1], b)); v = concat(v, digits(f[i,2], b));); vecsort(v) == vecsort(digits(n, b));} \\ _Michel Marcus_, Jul 14 2015
%Y A075047 Cf. A025283, A036057, A064818.
%K A075047 base,nonn
%O A075047 1,1
%A A075047 _Amarnath Murthy_, Sep 03 2002
%E A075047 More terms from _David Wasserman_, Jan 02 2005
%E A075047 a(14)-a(23) from _Donovan Johnson_, Oct 10 2009
%E A075047 a(24)-a(29) from _Robert G. Wilson v_, Jun 06 2014