

A075047


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


3



25, 121, 471663, 931225, 4473225, 6953931, 7301441, 10713728, 13246317, 17332133, 19367424, 34706961, 36310761, 54363717, 68714219, 73553125, 73641071, 74390183, 93478133, 102712448, 102941361, 109502361, 113162997, 115521875, 120934784, 134179011, 134381673, 134472875, 135478125
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OFFSET

1,1


COMMENTS

From Robert G. Wilson v, Jun 06 2014, updated Jun 10 2014: (Start)
The number of terms < 10^n: 0, 1, 2, 2, 2, 4, 7, 19, 71, 289, ..., .
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.
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, ..., .
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, ..., .
The least term with just four prime factors is 1713131455. By index, they are 110, 115, 251, ..., .
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, ..., .
So far ( < 10000000000) the count of digits 1,2,...,9,0 is {520, 271, 388, 254, 216, 211, 371, 172, 262, 117}.
(End)


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..1000 (first 311 terms from Robert G. Wilson v)


EXAMPLE

25 = 5^2 and 121 = 11^2 are terms.
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


MAPLE

with(numtheory): P:=proc(q) local a, b, c, d, k, n;
for n from 1 to q do a:=[]; b:=n; while b>0 do a:=[op(a), b mod 10]; b:=trunc(b/10); od;
b:=[]; c:=ifactors(n)[2]; for k from 1 to nops(c) do
d:=c[k, 1]; while d>0 do b:=[op(b), d mod 10]; d:=trunc(d/10); od; d:=c[k, 2];
while d>0 do b:=[op(b), d mod 10]; d:=trunc(d/10); od; od;
if nops(a)=nops(b) then a:=sort(a); b:=sort(b);
if a=b then print(n); fi; fi; od; end: P(10^10); # Paolo P. Lava, Jun 03 2014


MATHEMATICA

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 *)


PROG

(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


CROSSREFS

Cf. A025283, A036057, A064818.
Sequence in context: A085692 A087399 A030081 * A172047 A304422 A280390
Adjacent sequences: A075044 A075045 A075046 * A075048 A075049 A075050


KEYWORD

base,nonn


AUTHOR

Amarnath Murthy, Sep 03 2002


EXTENSIONS

More terms from David Wasserman, Jan 02 2005
a(14)a(23) from Donovan Johnson, Oct 10 2009
a(24)a(29) from Robert G. Wilson v, Jun 06 2014


STATUS

approved



