A059401 Numbers that contain as proper substrings every maximal prime power dividing them.

1197, 2510, 2570, 5210, 5230, 5290, 12590, 14673, 15230, 20530, 21530, 22510, 23510, 23570, 24590, 25030, 25210, 25310, 25390, 25430, 25490, 25510, 25570, 25790, 25910, 25930, 26570, 26590, 27530, 28510, 28570, 29530, 29570, 32510

Offset: 1

Author

Erich Friedman, Jan 29 2001

Keywords

• base
• nice
• nonn

Comments

Most terms end in 0, since 2*5*prime will work if prime contains 2 and 5 as substrings. The other terms are listed in A059402.

There must be at least two maximal prime powers dividing each term. - Harvey P. Dale, Dec 04 2016

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A141809, A010055.

Subsequence of A024619.

A059402 is a subsequence.

Equivalent sequence for primes instead of maximal prime powers: A050694.

Programs

Haskell

import Data.List (isInfixOf)
a059401 n = a059401_list !! (n-1)
a059401_list = filter (\x -> a010055 x == 0 &&
               all (`isInfixOf` show x) (map show $ a141809_row x)) [1..]
-- Reinhard Zumkeller, Dec 16 2013

Mathematica

psmppQ[n_]:=Module[{pp=#[[1]]^#[[2]]&/@FactorInteger[n], idn= IntegerDigits[ n]}, Length[pp]>1&&And@@Table[ SequenceCount[ idn, IntegerDigits[pp[[i]]]]>0,{i,Length[pp]}]]; Select[Range[ 33000], psmppQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 04 2016 *)

Extensions

Offset corrected by Reinhard Zumkeller, Dec 16 2013

Edited by Peter Munn, Sep 01 2022