A059401 - OEIS

%I #17 Sep 01 2022 12:09:39

%S 1197,2510,2570,5210,5230,5290,12590,14673,15230,20530,21530,22510,

%T 23510,23570,24590,25030,25210,25310,25390,25430,25490,25510,25570,

%U 25790,25910,25930,26570,26590,27530,28510,28570,29530,29570,32510

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

%C 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.

%C There must be at least two maximal prime powers dividing each term. - _Harvey P. Dale_, Dec 04 2016

%H Reinhard Zumkeller, <a href="/A059401/b059401.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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 *)

%o (Haskell)

%o import Data.List (isInfixOf)

%o a059401 n = a059401_list !! (n-1)

%o a059401_list = filter (\x -> a010055 x == 0 &&

%o                all (`isInfixOf` show x) (map show $ a141809_row x)) [1..]

%o -- _Reinhard Zumkeller_, Dec 16 2013

%Y Cf. A141809, A010055.

%Y Subsequence of A024619.

%Y A059402 is a subsequence.

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

%K base,nice,nonn

%O 1,1

%A _Erich Friedman_, Jan 29 2001

%E Offset corrected by _Reinhard Zumkeller_, Dec 16 2013

%E Edited by _Peter Munn_, Sep 01 2022