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 A033620 Numbers all of whose prime factors are palindromes. 9
 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 Index entries sequences related to prime factors FORMULA Sum_{n>=1} 1/a(n) = Product_{p in A002385} p/(p-1) = 5.0949... - Amiram Eldar, Sep 27 2020 EXAMPLE 10 = 2 * 5 is a term since both 2 and 5 are palindromes. 110 = 2 * 5 * 11 is a term since 2, 5 and 11 are palindromes. 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 (Python) from sympy import isprime, primefactors def pal(n): s = str(n); return s == s[::-1] def ok(n): return all(pal(f) for f in primefactors(n)) print(list(filter(ok, range(1, 132)))) # Michael S. Branicky, Apr 06 2021 CROSSREFS Cf. A002113, A002385, A046368, A051038. 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 28 22:22 EDT 2023. Contains 365739 sequences. (Running on oeis4.)