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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A141809, A010055.

Subsequence of A024619.

A059402 is a subsequence.

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

Sequence in context: A166221 A096955 A113898 * A059402 A252000 A251993

Adjacent sequences: A059398 A059399 A059400 * A059402 A059403 A059404

Keyword

base,nice,nonn

Author

Erich Friedman, Jan 29 2001

Extensions

Offset corrected by Reinhard Zumkeller, Dec 16 2013

Edited by Peter Munn, Sep 01 2022

Status

approved