A249097 - OEIS

A249097

Ordered union of the sets {h^6, h >=1} and {3*k^6, k >=1}.

1, 3, 64, 192, 729, 2187, 4096, 12288, 15625, 46656, 46875, 117649, 139968, 262144, 352947, 531441, 786432, 1000000, 1594323, 1771561, 2985984, 3000000, 4826809, 5314683, 7529536, 8957952, 11390625, 14480427, 16777216, 22588608, 24137569, 34012224, 34171875

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OFFSET

1,2

COMMENTS

Let S = {h^6, h >=1} and T = {3*k^6, k >=1}. Then S and T are disjoint. The position of n^6 in the ordered union of S and T is A249098(n), and the position of 3*n^6 is A249079(n).

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

EXAMPLE

{h^6, h >=1} = {1, 64, 729, 4096, 15625, 46656, 117649, ...};

{3*k^6, k >=1} = {3, 192, 2187, 12288, 46875, 139968, ...};

so the union is {1, 3, 64, 192, 729, 2187, 4096, 12288, ...}

PROG

(PARI) upto(n)=setunion(apply(k->k^6, [1..sqrtnint(n, 6)]), apply(k->3*k^6, [1..sqrtnint(n\3, 6)])) \\ Andrew Howroyd, Feb 18 2025

CROSSREFS

Cf. A001014, A249098, A249099, A249073.

Sequence in context: A053857 A175985 A037108 * A092901 A099338 A289668

Adjacent sequences: A249094 A249095 A249096 * A249098 A249099 A249100

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 21 2014

STATUS

approved