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 A334391 Numbers whose only palindromic divisor is 1. 3
 1, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 103, 107, 109, 113, 127, 137, 139, 149, 157, 163, 167, 169, 173, 179, 193, 197, 199, 211, 221, 223, 227, 229, 233, 239, 241, 247, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293, 299, 307 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equivalent: Numbers such that the LCM of their palindromic divisors (A087999) is 1, or, Numbers such that the number of palindromic divisors (A087990) is 1. All terms are odd. The 1st family consists of non-palindromic primes that form the subsequence A334321. The 2nd family consists of {p^k, p prime, k >= 2} such that p^j for 1 <= j <= k is not a palindrome {169 = 13^2, 289 = 17^2, 361 = 19^2, ..., 2197 = 13^3, ...} (see examples). The 3rd family consists of products p_1^q_1 * ... * p_k^q_k with k >= 2, all of whose divisors are nonpalindromic {221 = 13 * 27, 247 = 13 * 19, 299 = 13 * 23, 377 = 13 * 29, 391 = 17 * 23, 403 = 13 * 31, 481 = 13 * 37, ...}. LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 FORMULA A087990(a(n)) = 1. A087999(a(n)) = 1. EXAMPLE 49 = 7^2, the divisor 7 is a palindrome so 49 is not a term. 169 = 13^2, divisors of 169 are {1, 13, 169} and 169 is a term. 391 = 17*23, divisors of 391 are {1,17,23,391} and 391 is a term. 307^2 = 94249 that is palindrome, so 94249 is not a term. MAPLE notpali:= proc(n) local L;   L:= convert(n, base, 10);   L <> ListTools:-Reverse(L) end proc: filter:= proc(n) option remember; andmap(notpali, numtheory:-divisors(n) minus {1}) end proc: select(filter, [seq(i, i=1..400, 2)]); # Robert Israel, Apr 28 2020 MATHEMATICA Select[Range[300], !AnyTrue[Rest @ Divisors[#], PalindromeQ] &] (* Amiram Eldar, Apr 26 2020 *) PROG (PARI) ispal(n) = my(d=digits(n)); d == Vecrev(d); isok(n) = fordiv(n, d, if (d>1 && ispal(d), return(0))); return(1); \\ Michel Marcus, Apr 26 2020 (Python) from sympy.ntheory import divisors, is_palindromic def ok(n): return not any(is_palindromic(d) for d in divisors(n)[1:]) print(list(filter(ok, range(1, 308, 2)))) # Michael S. Branicky, May 08 2021 CROSSREFS A334321 is a subsequence. Cf. A008365, A087990, A087999, A334139. Sequence in context: A235154 A045921 A296520 * A334321 A034845 A241059 Adjacent sequences:  A334388 A334389 A334390 * A334392 A334393 A334394 KEYWORD nonn,base AUTHOR Bernard Schott, Apr 26 2020 STATUS approved

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Last modified July 28 14:19 EDT 2021. Contains 346335 sequences. (Running on oeis4.)