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A349094 a(n) = 2^(n-1) - tau(n) where tau(n) is the number of divisors of n. 0
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
Francis Laclé, Mar 25 2022
STATUS
approved

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Last modified February 22 02:30 EST 2024. Contains 370239 sequences. (Running on oeis4.)