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 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, 193117, 208174, 210181, 217894 (list; graph; refs; listen; history; text; internal format)
 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[ #[], {#[]}] & /@ FactorInteger@ n]}, While[ id[] == 0, id = Drop[id, 1]]; While[ s[] == 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 *) PROG (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)) print(list(filter(ok, range(220000)))) # Michael S. Branicky, Apr 22 2021 CROSSREFS Cf. A006753. Sequence in context: A343038 A359098 A218042 * A072434 A033285 A085109 Adjacent sequences: A176667 A176668 A176669 * A176671 A176672 A176673 KEYWORD nonn,base AUTHOR Paul Weisenhorn, Apr 23 2010 STATUS approved

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Last modified September 29 21:55 EDT 2023. Contains 365781 sequences. (Running on oeis4.)