

A340586


Perfect powers such that the two immediately adjacent perfect powers both have a largest exponent A025479 equal to 2.


3



8, 16, 169, 216, 343, 400, 441, 512, 625, 729, 841, 900, 1156, 1444, 1521, 1600, 1728, 1849, 1936, 2048, 2401, 2601, 2744, 2916, 3125, 3249, 3375, 3600, 3721, 3844, 4096, 4356, 4489, 4624, 4761, 4913, 5184, 5329, 5476, 5625, 5832, 6084, 6241, 6561, 6859, 7056
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..46.


EXAMPLE

a(1) = 8 because its neighboring perfect powers 4 = 2^2 and 9 = 3^2 both have the largest exponent 2.
9 is not in the sequence because both exponents of the neighboring perfect powers 8 = 2^3 and 16 = 2^4 are > 2.
a(2) = 16: neighbors 9 = 3^2 and 25 = 5^2 satisfy the exponent condition.
Next excluded terms: 25 (16 = 2^4, 27 = 3^3), 27 (32 = 2^5), 32 (27 = 3^3), 36 (32 = 2^5), 49 (64 = 2^6), 64 (81 = 3^4), 81 (64 = 2^6), 100 (81 = 3^4), 121 (125 = 5^3), 125 (128 = 2^7), 128 (125 = 5^3), 144 (128 = 2^7).
a(3) = 169: neighbors 144 = 12^2 and 196 = 14^2 satisfy the exponent condition.


PROG

(PARI) a340586(limit)={my(p2=999, p1=2, n2=1, n1=4); for(n=5, limit, my(p0=ispower(n)); if(p0>1, if(p2+p0==4, print1(n1, ", ")); n2=n1; n1=n; p2=p1; p1=p0))};
a340586(7500)


CROSSREFS

Cf. A000290, A001597, A025479, A111245, A153158, A340587, A340640, A340641.
Sequence in context: A323385 A061359 A330150 * A005445 A322342 A132377
Adjacent sequences: A340583 A340584 A340585 * A340587 A340588 A340589


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Jan 14 2021


STATUS

approved



