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

1197, 14673, 83731, 129717, 167835, 322794, 429635, 831328, 1127125, 1183497, 1184128, 1319825, 1344837, 1371294, 1724786, 1731195, 1943795, 2597175, 2971137, 2993715, 3161907, 3181437, 3719193, 4609731, 4913928, 5037365, 5912739, 5981125, 6193563

Offset: 1

Author

Erich Friedman, Jan 29 2001

Keywords

• base
• nice
• nonn

Examples

			1197 = 9 * 7 * 19 and all of these are substrings.
		

Links

• Reinhard Zumkeller and Donovan Johnson, Table of n, a(n) for n = 1..500 (first 100 terms from Reinhard Zumkeller)
• Reinhard Zumkeller, Demonstration of first 100 terms

Programs

Haskell

import Data.List (isInfixOf)
a059402 n = a059402_list !! (n-1)
a059402_list = filter chi [1..] where
  chi n = n `mod` 10 > 0 && f n 1 0 a000040_list where
    f :: Integer -> Integer -> Int -> [Integer] -> Bool
    f 1 1 o _    = o > 1
    f m x o ps'@(p:ps)
     | r == 0    = f m' (p*x) o ps'
     | x > 1     = show x `isInfixOf` show n && f m 1 (o+1) ps
     | m < p * p = f 1 m o ps
     | otherwise = f m 1 o ps
     where (m',r) = divMod m p
-- Reinhard Zumkeller, Jul 21 2011

Mathematica

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 *)

Python

from sympy import factorint
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

Extensions

Offset corrected and a(6)-a(26) from Donovan Johnson, Jul 09 2010

Definition stated more precisely by Reinhard Zumkeller, Jul 19 2011