A279537 -id:A279537 - cp's OEIS frontend

A343330 a(n) is the largest odd positive integer that is abundant and has the same prime signature as A279537(n) or 0 if no such integer exists.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 945, 0, 0, 2205, 0, 0, 2835, 0, 0, 15435, 0, 0, 8505, 0, 0, 108045, 0, 0, 11025, 25515, 0, 46305, 0, 0, 756315, 0, 0, 81675, 76545, 0, 324135, 0, 0, 5294205, 0, 0, 540225, 229635, 0, 2268945, 0, 0, 898425, 37059435, 0, 972405, 0, 3781575, 688905, 0, 0, 15882615, 0

Offset: 1

David A. Corneth, Apr 12 2021

nonn

Odd abundant numbers k have omega(k) >= 3. The zeros in this sequence come from numbers k having omega(k) < 3 in which case no positive integer with that prime signature exists.

Numbers with omega(k) > 3 are excluded by definition as most such numbers have infinitely many cases for that prime signature in which case no largest element exists.

			a(17) = 945 as A279537(17) = 120 = 2^(3) * 3^(1) * 5^(1) and has prime signature (3, 1, 1). The largest odd positive integer that has prime signature (3, 1, 1) and is abundant is 945.

A333964 Numbers of the form 2^i * 6^j * 30^k * 210^m where i, j, k, m >= 0.

Original entry on oeis.org

1, 2, 4, 6, 8, 12, 16, 24, 30, 32, 36, 48, 60, 64, 72, 96, 120, 128, 144, 180, 192, 210, 216, 240, 256, 288, 360, 384, 420, 432, 480, 512, 576, 720, 768, 840, 864, 900, 960, 1024, 1080, 1152, 1260, 1296, 1440, 1536, 1680, 1728, 1800, 1920, 2048, 2160, 2304, 2520, 2592

Offset: 1

David A. Corneth, Apr 20 2020

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A025487 and A002473.

Cf. A025610, A279537.

mx = 2600; Select[Sort[Flatten[Table[2^i*6^j*30^k*210^m, {i, 0, Log[2, mx]}, {j, 0, Log[6, mx]}, {k, 0, Log[30, mx]}, {m, 0, Log[210, mx]}]]], # <= mx &] (* Amiram Eldar, Apr 24 2020 after Robert G. Wilson v at A279537 *)

Sum_{n>=1} 1/a(n) = 15120/6061. - Amiram Eldar, Feb 18 2021

cp's OEIS Frontend

A343330 a(n) is the largest odd positive integer that is abundant and has the same prime signature as A279537(n) or 0 if no such integer exists.

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A333964 Numbers of the form 2^i * 6^j * 30^k * 210^m where i, j, k, m >= 0.

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