A046349 Composite numbers with only palindromic prime factors.

4, 6, 8, 9, 10, 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, 105, 108, 110, 112, 120, 121, 125, 126, 128, 132, 135, 140, 144, 147, 150

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn
• base
• easy

Links

• Robert Israel, Table of n, a(n) for n = 1..3020

Crossrefs

Cf. A002385, A033620, A046350, A046351.

Programs

Maple

isA046349 := proc(n)
    simplify(isA033620(n) and not isprime(n)) ;
end proc:
for n from 2 to 300 do
    if isA046349(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[4,150],!PrimeQ[#]&&And@@palQ/@First/@FactorInteger[#]&] (* Jayanta Basu, Jun 05 2013 *)
Select[Range[200],CompositeQ[#]&&AllTrue[FactorInteger[#][[All,1]],PalindromeQ]&] (* Harvey P. Dale, May 15 2022 *)

Python

from sympy import isprime, primefactors
def pal(n): s = str(n); return s == s[::-1]
def ok(n): return not isprime(n) and all(pal(f) for f in primefactors(n))
print(list(filter(ok, range(4, 151)))) # Michael S. Branicky, Apr 06 2021

Formula

A033620 INTERSECT A002808. - R. J. Mathar, Sep 09 2015