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A059401 Numbers that contain as proper substrings every maximal prime power dividing them. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 5 10:54 EDT 2022. Contains 357255 sequences. (Running on oeis4.)