A242418 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.

1, 2, 4, 6, 8, 10, 14, 16, 22, 26, 30, 32, 34, 36, 38, 46, 58, 62, 64, 74, 82, 86, 90, 94, 100, 106, 110, 118, 122, 128, 134, 142, 146, 158, 166, 178, 194, 196, 202, 206, 210, 214, 216, 218, 226, 238, 254, 256, 262, 270, 274, 278, 298, 300, 302, 314, 326, 334

Offset

1,2

Comments

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..1200

Formula

a(1)=1, and for n > 1, a(n) = 2 * A241912(n-1).

Mathematica

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 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A242418 (FIXED-POINTS 1 1 A137502))
;; Alternatively:
(define (A242418 n) (if (= 1 n) n (* 2 (A241912 (- n 1)))))

Crossrefs

Fixed points of A137502.

Cf. A241912.

A002110 and A079704 are subsequences.

Sequence in context: A180081 A340854 A367586 * A191146 A220850 A151566

Adjacent sequences: A242415 A242416 A242417 * A242419 A242420 A242421

Keyword

nonn

Author

Antti Karttunen, May 20 2014

Status

approved