

A176670


Composite numbers having the same digits as their prime factors (with multiplicity), excluding zero digits.


12



1111, 1255, 12955, 17482, 25105, 28174, 51295, 81229, 91365, 100255, 101299, 105295, 107329, 110191, 110317, 117067, 124483, 127417, 129595, 132565, 137281, 145273, 146137, 149782, 163797, 171735, 174082, 174298, 174793, 174982
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OFFSET

1,1


COMMENTS

Subsequence of A006753 (Smith numbers).
These numbers still need a better name.  Ely Golden, Dec 25 2016
Terms of this sequence never have more zero digits than their prime factors.  Ely Golden, Jan 10 2017


LINKS

Ely Golden, Table of n, a(n) for n = 1..10000 [Terms 1 through 2113 were computed by Paul Weisenhorn; and terms 2114 to 10000 by Ely Golden, Nov 30 2016]
Ely Golden, Smith number sequence generator optimized for A176670
Ely Golden, Proof that A280827(n)>=0 for all n>1
Eric W. Weisstein, Smith Number


EXAMPLE

n = 25105 = 5*5021; both n and the factorization of n have digits 1, 2, 5, 5; sorted and excluding zeros.
n = 110191 = 101*1091; both n and the factorization of n have digits 1, 1, 1, 1, 9; sorted and excluding zeros.
n = 171735 = 3*5*107*107; both n and the factorization of n have digits 1, 1, 3, 5, 7, 7; sorted and excluding zeros.


MATHEMATICA

fQ[n_] := Block[{id = Sort@ IntegerDigits@ n, s = Sort@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@ n]}, While[ id[[1]] == 0, id = Drop[id, 1]]; While[ s[[1]] == 0, s = Drop[s, 1]]; n > 1 && ! PrimeQ@ n && s == id]; Select[ Range@ 200000, fQ]
Select[Range[2*10^5], Function[n, And[CompositeQ@ n, Sort@ DeleteCases[#, 0] &@ IntegerDigits@ n == Sort@ DeleteCases[#, 0] &@ Flatten@ Map[IntegerDigits@ ConstantArray[#1, #2] & @@ # &, FactorInteger@ n]]]] (* Michael De Vlieger, Dec 10 2016 *)


CROSSREFS

Cf. A006753.
Sequence in context: A290848 A290556 A218042 * A072434 A033285 A085109
Adjacent sequences: A176667 A176668 A176669 * A176671 A176672 A176673


KEYWORD

nonn,base


AUTHOR

Paul Weisenhorn, Apr 23 2010


STATUS

approved



