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A176670
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Composite numbers having the same digits as their prime factors (with multiplicity), excluding zero digits.
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12
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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, 193117, 208174, 210181, 217894
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(Python)
from sympy import factorint, flatten
def sd(n): return sorted(str(n).replace('0', ''))
def ok(n):
f = factorint(n)
return sum(f[p] for p in f) > 1 and sd(n) == sorted(flatten(sd(p)*f[p] for p in f))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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