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A318298
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Numbers whose set of decimal digits coincides with the set of the indices of their prime factors.
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2
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12, 14, 154, 1196, 14112, 21888, 53625, 226512, 279174, 358435, 821142, 1222452, 1665664, 2228814, 2454375, 2614248, 2872116, 4425729, 5751746, 8653645, 9551256, 15261246, 19427226, 19644898, 19775998, 21271488, 27676935, 29591892, 29956212, 41878242, 45574144
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OFFSET
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1,1
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COMMENTS
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It is impossible to find a number with 9 distinct decimal digits because the prime factors 2 and 5 generate d_k = 0.
The finite subsequence containing the smallest numbers having at least j distinct digits for j = 2, 3, ..., 8, is 12, 154, 53625, 279174, 19427226, 82447365 and 41762985264.
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LINKS
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Giovanni Resta, Table of n, a(n) for n = 1..10000
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EXAMPLE
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1196 is in the sequence because the prime factors are {2, 13, 23} = {prime(1), prime(6), prime(9)}, and 1196 contains the decimal digits 1, 6, 9.
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MAPLE
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with(numtheory):nn:=10^8:
for n from 1 to nn do:
lst:={}:d:=factorset(n):n0:=nops(d):
q:=convert(n, base, 10):n1:=nops(q):
p:=product(‘q[i]’, ‘i’=1..n1):
if p<>0
then
for i from 1 to n1 do :
lst:=lst union {ithprime(q[i])}:
od:
if lst = d
then
print(n):
else
fi:fi:
od:
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MATHEMATICA
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ok[n_] := Block[{f = First /@ FactorInteger[n], d}, Last@f < 24 && Min[d = Union@ IntegerDigits@ n] > 0 && Prime[d] == f]; Select[Range[10^6], ok] (* Giovanni Resta, Aug 24 2018 *)
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CROSSREFS
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Cf. A001221, A080683, A097227, A290675.
Sequence in context: A058951 A287916 A002926 * A139310 A221819 A329026
Adjacent sequences: A318295 A318296 A318297 * A318299 A318300 A318301
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KEYWORD
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nonn,base
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AUTHOR
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Michel Lagneau, Aug 24 2018
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STATUS
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approved
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