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A033620 Numbers all of whose prime factors are palindromes. 7
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 98, 99, 100, 101, 105, 108, 110, 112, 120, 121, 125, 126, 128, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multiplicative closure of A002385; A051038 and A046368 are subsequences. [Reinhard Zumkeller, Apr 11 2011]

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10550

MAPLE

N:= 5: # to get all terms of up to N digits

digrev:= proc(t) local L; L:= convert(t, base, 10);

add(L[-i-1]*10^i, i=0..nops(L)-1);

end proc:

PPrimes:= [2, 3, 5, 7, 11]:

for d from 3 to N by 2 do

    m:= (d-1)/2;

    PPrimes:= PPrimes, select(isprime, [seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1)]);

od:

PPrimes:= map(op, [PPrimes]):

M:= 10^N:

B:= Vector(M);

B[1]:= 1:

for p in PPrimes do

  for k from 1 to floor(log[p](M)) do

     R:= [$1..floor(M/p^k)];

     B[p^k*R] := B[p^k*R] + B[R]

  od

od:

select(t -> B[t] > 0, [$1..M]); # Robert Israel, Jul 05 2015

# alternative

isA033620:= proc(n)

    for d in numtheory[factorset](n) do

        if not isA002113(op(1, d)) then

            return false;

        end if;

    end do;

    true ;

end proc:

for n from 1 to 300 do

    if isA033620(n) then

        printf("%d, ", n) ;

    end if;

end do: # R. J. Mathar, Sep 09 2015

MATHEMATICA

palQ[n_]:=Reverse[x=IntegerDigits[n]]==x; Select[Range[131], And@@palQ/@First/@FactorInteger[#]&] (* Jayanta Basu, Jun 05 2013 *)

PROG

(Haskell)

a033620 n = a033620_list !! (n-1)

a033620_list = filter chi [1..] where

   chi n = a136522 spf == 1 && (n' == 1 || chi n') where

      n' = n `div` spf

      spf = a020639 n  -- cf. A020639

-- Reinhard Zumkeller, Apr 11 2011

(PARI) ispal(n)=n=digits(n); for(i=1, #n\2, if(n[i]!=n[#n+1-i], return(0))); 1

is(n)=if(n<13, n>0, vecmin(apply(ispal, factor(n)[, 1]))) \\ Charles R Greathouse IV, Feb 06 2013

CROSSREFS

Sequence in context: A317469 A194424 A033892 * A033637 A084034 A084347

Adjacent sequences:  A033617 A033618 A033619 * A033621 A033622 A033623

KEYWORD

nonn,base,easy

AUTHOR

N. J. A. Sloane, May 17 1998

STATUS

approved

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Last modified September 25 21:12 EDT 2018. Contains 315425 sequences. (Running on oeis4.)