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A349094 a(n) = 2^(n-1) - tau(n) where tau(n) is the number of divisors of n. 0

%I #27 May 11 2022 14:51:27

%S 0,0,2,5,14,28,62,124,253,508,1022,2042,4094,8188,16380,32763,65534,

%T 131066,262142,524282,1048572,2097148,4194302,8388600,16777213,

%U 33554428,67108860,134217722,268435454,536870904,1073741822,2147483642,4294967292,8589934588

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

%C 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.

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

%e 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.

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

%K nonn,easy

%O 1,3

%A _Francis Laclé_, Mar 25 2022

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Last modified April 15 13:47 EDT 2024. Contains 371689 sequences. (Running on oeis4.)