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A059402 Numbers with more than one prime factor that do not end in 0 and contain as substrings every maximal prime power dividing them.

%I A059402 #27 Aug 14 2021 07:12:18
%S A059402 1197,14673,83731,129717,167835,322794,429635,831328,1127125,1183497,
%T A059402 1184128,1319825,1344837,1371294,1724786,1731195,1943795,2597175,
%U A059402 2971137,2993715,3161907,3181437,3719193,4609731,4913928,5037365,5912739,5981125,6193563
%N A059402 Numbers with more than one prime factor that do not end in 0 and contain as substrings every maximal prime power dividing them.
%H A059402 Reinhard Zumkeller and Donovan Johnson, <a href="/A059402/b059402.txt">Table of n, a(n) for n = 1..500</a> (first 100 terms from Reinhard Zumkeller)
%H A059402 Reinhard Zumkeller, <a href="/A059402/a059402.txt">Demonstration of first 100 terms</a>
%e A059402 1197 = 9 * 7 * 19 and all of these are substrings.
%t A059402 ok[n_] := If[id = IntegerDigits[n]; Last[id] == 0, False, If[ff = IntegerDigits /@ Apply[ Power, FactorInteger[n], {1}]; Length[ff] == 1, False, And @@ (MatchQ[id, {___, Sequence @@ #, ___}] & ) /@ ff]]; A059402 = {}; Do[ If[ok[n], Print[n]; AppendTo[A059402, n]], {n, 1, 6*10^6}] (* _Jean-François Alcover_, Nov 24 2011 *)
%o A059402 (Haskell)
%o A059402 import Data.List (isInfixOf)
%o A059402 a059402 n = a059402_list !! (n-1)
%o A059402 a059402_list = filter chi [1..] where
%o A059402   chi n = n `mod` 10 > 0 && f n 1 0 a000040_list where
%o A059402     f :: Integer -> Integer -> Int -> [Integer] -> Bool
%o A059402     f 1 1 o _    = o > 1
%o A059402     f m x o ps'@(p:ps)
%o A059402      | r == 0    = f m' (p*x) o ps'
%o A059402      | x > 1     = show x `isInfixOf` show n && f m 1 (o+1) ps
%o A059402      | m < p * p = f 1 m o ps
%o A059402      | otherwise = f m 1 o ps
%o A059402      where (m',r) = divMod m p
%o A059402 -- _Reinhard Zumkeller_, Jul 21 2011
%o A059402 (Python)
%o A059402 from sympy import factorint
%o A059402 A059402_list = [n for n in range(2,10**6) if n % 10 and len(factorint(n)) > 1 and all(str(a**b) in str(n) for a, b in factorint(n).items())] # _Chai Wah Wu_, Aug 13 2021
%K A059402 base,nice,nonn
%O A059402 1,1
%A A059402 _Erich Friedman_, Jan 29 2001
%E A059402 Offset corrected and a(6)-a(26) from _Donovan Johnson_, Jul 09 2010
%E A059402 Definition stated more precisely by _Reinhard Zumkeller_, Jul 19 2011