A190150 -id:A190150 - cp's OEIS frontend

A190149 Even numbers n (written in binary) such that in base-2 lunar arithmetic, the sum of the divisors of n is a number containing a 0 (in binary).

10010, 100010, 100110, 110010, 1000010, 1000100, 1000110, 1001010, 1001110, 1010010, 1100010, 1100110, 1110010, 10000010, 10000100, 10000110, 10001010, 10001100, 10001110, 10010010, 10010110, 10011010, 10011110, 10100010, 10100110, 10110010, 11000010, 11000100, 11000110, 11001010, 11001110, 11010010, 11100010, 11100110, 11110010, 100000010, 100000100

Offset: 1

N. J. A. Sloane, May 05 2011

As remarked in A188548, if n is even then most of the time A188548(n) = 111...111 (that is, a number of the form 2^k-1). This sequence lists the exceptions.

			In base-2 lunar arithmetic, the divisors of 10010 are 1, 10, 1001 and 10010, whose sum is 11011.

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun, and N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A188548, A067399. See A190150 and A190151 for the base-10 representation of these numbers.

A190151 A190149 converted to base 10 and halved.

Original entry on oeis.org

9, 17, 19, 25, 33, 34, 35, 37, 39, 41, 49, 51, 57, 65, 66, 67, 69, 70, 71, 73, 75, 77, 79, 81, 83, 89, 97, 98, 99, 101, 103, 105, 113, 115, 121, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 141, 142, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 162, 163, 165, 167, 169, 177, 179, 185, 193, 194, 195, 197, 198, 199, 201, 203, 205, 207, 209, 211

Offset: 1

N. J. A. Sloane, May 05 2011

Take the even numbers n such that in base 2 lunar arithmetic, the sum of the divisors of n is not of the form 2^k-1, and divide them (in ordinary arithmetic) by 2 (cf. A190149, A190150)

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Index entries for sequences related to dismal (or lunar) arithmetic

Cf. A188548, A190149, A190150.

cp's OEIS Frontend

A190149 Even numbers n (written in binary) such that in base-2 lunar arithmetic, the sum of the divisors of n is a number containing a 0 (in binary).

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