A349094 a(n) = 2^(n-1) - tau(n) where tau(n) is the number of divisors of n.

0, 0, 2, 5, 14, 28, 62, 124, 253, 508, 1022, 2042, 4094, 8188, 16380, 32763, 65534, 131066, 262142, 524282, 1048572, 2097148, 4194302, 8388600, 16777213, 33554428, 67108860, 134217722, 268435454, 536870904, 1073741822, 2147483642, 4294967292, 8589934588

Offset

1,3

Comments

Considering that there are 2^(n-1) compositions (ordered partitions) of n, then tau(n) represents the number of compositions whose terms are all equal. Subtracting tau(n) from 2^(n-1) gives the number of compositions whose terms are not all equal.

Links

Table of n, a(n) for n=1..34.

Formula

a(n) = A011782(n) - A000005(n).

Example

For n = 6, a(6) = 28 because from all the possible compositions (32 in this case) there are four whose terms are equal: 6, 3+3, 2+2+2, 1+1+1+1+1+1.

Crossrefs

Cf. A000005 (tau), A011782 (number of compositions).

Sequence in context: A100779 A212346 A194124 * A212340 A304719 A022630

Adjacent sequences: A349091 A349092 A349093 * A349095 A349096 A349097

Keyword

nonn,easy

Author

Francis Laclé, Mar 25 2022

Status

approved