A340640 -id:A340640 - cp's OEIS frontend

A340641 a(n) is the least root of A340640(n).

2, 3, 5, 3, 2, 6, 7, 2, 3, 10, 11, 5, 2, 12, 14, 15, 3, 2, 17, 18, 19, 22, 23, 24, 26, 28, 31, 10, 2, 33, 35, 6, 11, 37, 41, 42, 45, 46, 3, 13, 47, 48, 50, 52, 53, 55, 56, 58, 59, 63, 65, 70, 71, 76, 77, 80, 82, 83, 88, 89, 90, 91, 96, 97, 99, 101, 103, 104, 110

Offset: 1

Hugo Pfoertner, Jan 14 2021

nonn

			a(1) = 2: A340640(1) = 4 = 2^2;
a(2) = 3: A340640(2) = 9 = 3^2;
a(3) = 5: A350640(3) = 25 = 5^2;
a(4) = 3: A340640(4) = 27 = 3^3.

Cf. A025478, A340587, A340640.

a340641(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(round(n1^(1/p1)), ", ")); n2=n1; n1=n; p2=p1; p1=p0))};
a340641(13000)

a(n) = A025478(A340640(n)).

A340586 Perfect powers such that the two immediately adjacent perfect powers both have a largest exponent A025479 equal to 2.

Original entry on oeis.org

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

Offset: 1

Hugo Pfoertner, Jan 14 2021

nonn

			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.

Cf. A000290, A001597, A025479, A111245, A153158, A340587, A340640, A340641.

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)

cp's OEIS Frontend

A340641 a(n) is the least root of A340640(n).

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