A328045 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A328045

a(n) = smallest m for which there is a sequence n = b_1 < b_2 < ... < b_t = m such that b_1^c_1*b_2^c_2*...*b_t^c_t is a fourth power, with all c_i < 4.

0, 1, 4, 6, 4, 10, 9, 14, 15, 9, 18, 22, 20, 26, 21, 24, 16, 34, 27, 38, 25, 28, 33, 46, 30, 25, 39, 35, 36, 58, 40, 62, 42, 44, 51, 45, 36, 74, 57, 52, 49, 82, 50, 86, 55, 54, 69, 94, 54, 49, 63, 68, 65, 106, 70, 66, 64, 76, 87, 118, 75, 122, 93, 77, 64, 78

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

a(n) = n if and only if n is a perfect square.

a(n) >= n + A300518(n) if n is not a perfect square.

a(n) <= A006255(n), and a(n) = A006255(n) except for when n is in A328218, a subsequence of A269045.

LINKS

Peter Kagey, Table of n, a(n) for n = 0..500

EXAMPLE

For n = 1, a(1) = 1 with sequence 1 = 1^4.

For n = 2, a(2) = 4 with sequence 2^2 * 4 = 2^4.

For n = 3, a(3) = 6 with sequence 3^2 * 4 * 6^2 = 6^4.

For n = 4, a(4) = 4 with sequence 4^2 = 2^4.

For n = 5, a(5) = 10 with sequence 5 * 8^3 * 10^3 = 40^4.

For n = 6, a(6) = 9 with sequence 6^2 * 8^2 * 9 = 12^4.

For n = 7, a(7) = 14 with sequence 7^2 * 8^2 * 14^2 = 28^4.

CROSSREFS

Cf. A006255 (square), A277494 (cube).

Cf. A269045, A300518, A328218.

Sequence in context: A349093 A143545 A338155 * A277278 A328722 A143521

Adjacent sequences: A328042 A328043 A328044 * A328046 A328047 A328048

KEYWORD

nonn

AUTHOR

Peter Kagey, Oct 02 2019

STATUS

approved