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%I #13 Aug 27 2016 09:57:04
%S 1,2,4,6,8,10,14,16,22,26,30,32,34,36,38,46,58,62,64,74,82,86,90,94,
%T 100,106,110,118,122,128,134,142,146,158,166,178,194,196,202,206,210,
%U 214,216,218,226,238,254,256,262,270,274,278,298,300,302,314,326,334
%N Numbers n in whose prime factorization, n = 2^e1 * 3^e2 * 5^e3 * ... * p_k^e_k, the exponents (some of them possibly zero) of prime factors from 2 to p_k form a palindrome, so that e1 = e_k, e2 = e_{k-1}, etc.
%C a(1)=1 is included because 1 has an empty factorization (either no exponents, or all of them are zero), which thus is also a palindrome.
%H Antti Karttunen, <a href="/A242418/b242418.txt">Table of n, a(n) for n = 1..1200</a>
%F a(1)=1, and for n > 1, a(n) = 2 * A241912(n-1).
%t f[n_] := If[n == 1, {0}, Function[f, ReplacePart[Table[0, {PrimePi[f[[-1, 1]]]}], #] &@ Map[PrimePi@ First@ # -> Last@ # &, f]]@ FactorInteger@ n]; g[w_List] := Times @@ Flatten@ MapIndexed[Prime[#2]^#1 &, w]; Select[Range@ 336, g@ f@ # == g@ Reverse@ f@ # &] (* _Michael De Vlieger_, Aug 27 2016 *)
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A242418 (FIXED-POINTS 1 1 A137502))
%o ;; Alternatively:
%o (define (A242418 n) (if (= 1 n) n (* 2 (A241912 (- n 1)))))
%Y Fixed points of A137502.
%Y Cf. A241912.
%Y A002110 and A079704 are subsequences.
%K nonn
%O 1,2
%A _Antti Karttunen_, May 20 2014
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