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, 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 *)
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
KEYWORD
nonn,base
AUTHOR
Paul Weisenhorn, Apr 23 2010
STATUS
approved