A065879 -id:A065879 - cp's OEIS frontend

A272759 a(n) = A065879(n)/n.

1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 5, 2, 0, 3, 4, 1, 2, 2, 0, 2, 6, 5, 3, 2, 0, 0, 3, 3, 4, 4, 5, 1, 2, 2, 0, 2, 5, 0, 4, 2, 5, 6, 4, 5, 4, 3, 0, 2, 0, 0, 4, 0, 4, 3, 0, 3, 4, 4, 5, 4, 6, 5, 6, 1, 2, 2, 0, 2, 5, 0, 4, 2, 6, 5, 4, 0, 4, 4, 5, 2, 5, 5, 4, 6, 4, 4, 3

Offset: 1

Peter Kagey, May 05 2016

This sequence is bounded above by A272756.

a(n) is the least value i such that A000120(n * i) = i or 0 if no such value exists.

Peter Kagey, Table of n, a(n) for n = 1..10000

Cf. A000120, A065879, A272756, A272760.

Table[(SelectFirst[Range[2^12], # == n First@ DigitCount[#, 2] &] /.
    k_ /; MissingQ@ k -> 0)/n, {n, 120}] (*  *)

A272761 List of indices i such that A065879(i) != A065880(i).

Original entry on oeis.org

23, 27, 37, 41, 46, 53, 54, 57, 69, 71, 74, 77, 79, 81, 82, 83, 85, 89, 91, 92, 101, 105, 106, 107, 108, 113, 114, 121, 125, 133, 135, 138, 139, 141, 142, 143, 147, 148, 153, 154, 158, 161, 162, 163, 164, 166, 167, 169, 170, 173, 177, 178, 181, 182, 184, 197

Offset: 1

Peter Kagey, May 06 2016

Equivalently a list of indices i such that A272759(i) != A272760(i).

Also, a list of indices i such that A065413(i) > 1.

Peter Kagey, Table of n, a(n) for n = 1..10000

Cf. A065879, A065880, A065413, A272759, A272760.

A065880 Largest positive number that is n times the number of 1's in its binary expansion, or 0 if no such number exists.

Original entry on oeis.org

0, 1, 2, 6, 4, 10, 12, 21, 8, 18, 20, 55, 24, 0, 42, 60, 16, 34, 36, 0, 40, 126, 110, 115, 48, 0, 0, 108, 84, 116, 120, 155, 32, 66, 68, 0, 72, 222, 0, 156, 80, 246, 252, 172, 220, 180, 230, 0, 96, 0, 0, 204, 0, 318, 216, 0, 168, 285, 232, 295, 240, 366, 310, 378, 64, 130

Offset: 0

Henry Bottomley, Nov 26 2001

a(n) is bounded above by n*A272756(n), so a program only has to check values up to that point to see if a(n) is zero. - Peter Kagey, May 05 2016

			a(23)=115 since 115 is written in binary as 1110011 and 115/(1+1+1+0+0+1+1)=23 and there is no higher possibility (if k is more than 127 then k divided by its number of binary 1's is more than 26).

Peter Kagey, Table of n, a(n) for n = 0..10000

A052489 is the base 10 equivalent.

Cf. A000120, A049445, A058898, A065413, A065878, A065879, A272756.

Table[SelectFirst[Reverse@ Range@ #, First@ DigitCount[#, 2] == #/n &] &[n SelectFirst[Range[2^12], # > IntegerLength[n #, 2] &]], {n, 80}] /. k_ /; MissingQ@ k -> 0 (* Michael De Vlieger, May 05 2016, Version 10.2 *)

A065878 Numbers which are not an integer multiple of their number of binary 1's.

Original entry on oeis.org

3, 5, 7, 9, 11, 13, 14, 15, 17, 19, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 65, 67, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89, 90, 91, 93, 94, 95, 97, 98, 99, 100

Offset: 1

Henry Bottomley, Nov 26 2001

			5 is in the sequence since 5 = 101_2 and 5 is not a multiple of 1 + 0 + 1 = 2.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Complement of A049445.
The base-10 equivalent is A065877.
Cf. A000120, A058898, A065413, A065879, A065880.

Select[Range[100],!IntegerQ[#/Total[IntegerDigits[#,2]]]&]  (* Harvey P. Dale, Apr 20 2011 *)

isok(k) = k % hammingweight(k); \\ Amiram Eldar, Aug 04 2025

cp's OEIS Frontend

A272759 a(n) = A065879(n)/n.

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A272761 List of indices i such that A065879(i) != A065880(i).

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A065880 Largest positive number that is n times the number of 1's in its binary expansion, or 0 if no such number exists.

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A065878 Numbers which are not an integer multiple of their number of binary 1's.

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