OFFSET
1,1
COMMENTS
Equivalently: numbers m with only one prime factor such that the LCM of their palindromic divisors is neither 1 nor m: subsequence of A334392.
G. J. Simmons conjectured there are no palindromes of form n^k for k >= 5 (and n > 1) (see Simmons p. 98). According to this conjecture, these perfect powers are terms: {2^k, k>=4}, {3^k, k>=3}, {5^k, k>=2}, {7^k, k=2 and k>=4}, {11^k, k>=5}, {101^k, k>= 5}, {131^k, k>=2}, ...
REFERENCES
Murray S. Klamkin, Problems in applied mathematics: selections from SIAM review, (1990), p. 520.
LINKS
Gustavus J. Simmons, Palindromic Powers, J. Rec. Math., 3 (No. 2, 1970), 93-98 [Annotated scanned copy].
Wikipedia, Palindromic number, Perfect Powers.
EXAMPLE
5^2 = 25, 2^6 = 64, 3^4 = 81 are terms.
7^2 = 49 is a term, 7^3 = 343 is not a term, and 7^4 = 2401 is a term.
101^2 = 10201 and 11^4 = 14641 are not terms.
MATHEMATICA
q[n_] := Module[{f = FactorInteger[n]}, Length[f] == 1 && f[[1, 2]] > 1 && PalindromeQ[f[[1, 1]]]]; Select[Range[10^5], !PalindromeQ[#] && q[#] &] (* Amiram Eldar, Dec 10 2020 *)
PROG
(PARI) ispal(n) = my(d=digits(n)); Vecrev(d)==d;
isok(k) = my(p); isprimepower(k, &p) && isprime(p) && ispal(p) &&!ispal(k); \\ Michel Marcus, Dec 10 2020
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Dec 10 2020
EXTENSIONS
More terms from Amiram Eldar, Dec 10 2020
STATUS
approved