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

1,1

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

Sequence in context: A096955 A113898 A059401 * A252000 A251993 A250379

Adjacent sequences: A059399 A059400 A059401 * A059403 A059404 A059405

Keyword

base,nice,nonn

Author

Erich Friedman, Jan 29 2001

Extensions

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

Definition stated more precisely by Reinhard Zumkeller, Jul 19 2011

Status

approved