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 A244423 Nonprime palindromes n such that the product of divisors of n is also a palindrome. 2
 1, 4, 22, 111, 121, 202, 1001, 1111, 10001, 10201, 11111, 100001, 1000001, 1001001, 1012101, 1100011, 1101011, 1111111, 10000001, 100000001, 101000101, 110000011, 200010002, 10000000001, 10011111001, 11000100011, 11001010011, 11100100111, 11101010111, 20000100002 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Primes trivially satisfy this property and are therefore not included in the sequence. These are the palindromes in A244411. LINKS Chai Wah Wu, Table of n, a(n) for n = 1..49 Eric Weisstein's World of Mathematics, Palindromic Number EXAMPLE The divisors of 22 are 1, 2, 11 and 22. 1*2*11*22 = 484 is a palindrome. Since 22 is also a palindrome, 22 is a member of this sequence. MAPLE with(numtheory); P:=proc(q) local a, b, c, k, n; for n from 1 to q do if not isprime(n) then a:=n; b:=0; while a>0 do b:=b*10+(a mod 10); a:=trunc(a/10); od; if b=n then a:=divisors(n); b:=mul(a[k], k=1..nops(a)); a:=b; c:=0; while a>0 do c:=c*10+(a mod 10); a:=trunc(a/10); od; if c=b then print(n); fi; fi; fi; od; end: P(10^9); # Paolo P. Lava, Jul 04 2014 MATHEMATICA palQ[n_] := Block[{d = IntegerDigits@ n}, Reverse@ d == d]; lim = 15000000; Select[Complement[Range@ lim, Prime@ Range@ PrimePi@ lim], And[palQ@ #, palQ[Times @@ Divisors@ #]] &] (* Michael De Vlieger, Aug 25 2015 *) Select[Range[200002*10^5], !PrimeQ[#]&&AllTrue[{#, Times@@Divisors[#]}, PalindromeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 28 2020 *) PROG (PARI) rev(n)={r=""; dig=digits(n); for(i=1, #dig, r=concat(Str(dig[i]), r)); return(eval(r))} for(n=1, 10^8, if(rev(n)==n&&(!isprime(n)), d=divisors(n); ss=prod(j=1, #d, d[j]); if(ss==rev(ss), print1(n, ", ")))) (PARI) /* david(n) returns the n-th palindrome from David A. Corneth, Jun 06 2014 */ david(n)={my(d, i, r); r=vector(#digits(n-10^(#digits(n\11)))+#digits(n\11)); n=n-10^(#digits(n\11)); d=digits(n); for(i=1, #d, r[i]=d[i]; r[#r+1-i]=d[i]); sum(i=1, #r, 10^(#r-i)*r[i])} rev(n)={r=""; dig=digits(n); for(i=1, #dig, r=concat(Str(dig[i]), r)); return(eval(r))} for(n=2, 10^6, pal=david(n); if(!isprime(pal), d=divisors(pal); ss=prod(j=1, #d, d[j]); if(ss==rev(ss), print1(pal, ", ")))) (Python) import sympy from sympy import isprime from sympy import divisors def rev(n): ..r = "" ..for i in str(n): ....r = i + r ..return int(r) def a(): ..for n in range(1, 10**8): ....if rev(n) == n and not isprime(n): ......p = 1 ......for i in divisors(n): ........p*=i ......if rev(p)==p: ........print(n, end=', ') a() (Python) from sympy import divisor_count, sqrt def palgen(l, b=10): # generator of palindromes in base b of length <= 2*l     if l > 0:         yield 0         for x in range(1, l+1):             n = b**(x-1)             n2 = n*b             for y in range(n, n2):                 k, m = y//b, 0                 while k >= b:                     k, r = divmod(k, b)                     m = b*m + r                 yield y*n + b*m + k             for y in range(n, n2):                 k, m = y, 0                 while k >= b:                     k, r = divmod(k, b)                     m = b*m + r                 yield y*n2 + b*m + k A244423_list = [1] for n in palgen(6):     d = divisor_count(n)     if d > 2:         q, r = divmod(d, 2)         s = str(n**q*(sqrt(n) if r else 1))         if s == s[::-1]:             A244423_list.append(n) # Chai Wah Wu, Aug 25 2015 CROSSREFS Cf. A244411, A002113. Sequence in context: A007994 A006651 A159616 * A144047 A077543 A084157 Adjacent sequences:  A244420 A244421 A244422 * A244424 A244425 A244426 KEYWORD nonn,base AUTHOR Derek Orr, Jun 27 2014 EXTENSIONS Edited name by Chai Wah Wu, Aug 25 2015 STATUS approved

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Last modified September 18 10:11 EDT 2020. Contains 337166 sequences. (Running on oeis4.)