|
|
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
|
|
|
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..]
|
|
CROSSREFS
|
Equivalent sequence for primes instead of maximal prime powers: A050694.
|
|
KEYWORD
|
base,nice,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|