A107949 - OEIS

%I #6 Jun 13 2017 06:50:39

%S 1,2,4,7,14,27,54

%N Smallest k_n such that there exist positive integers 0 < k_1 < ... < k_n such that there exists only one n-tuple of nonnegative integers (b_1, ..., b_n) - namely (1, ..., 1) - such that the sum of the b_i's equals n and the sum of the b_i*k_i's equals the sum of the k_i's.

%C These are instances that show that the sequence is at most what is given: 1, 1+2, 1+2+4, 1+2+5+7, 1+2+6+12+14, 1+3+11+22+23+27, 1+2+6+22+44+46+54.

%e a(3)=4 because 1+2+3 = 2+2+2 but you can't write 1+2+4 as the sum of three numbers in {1,2,4} in another way.

%e a(4)=7 because, for instance, 2+4+5+6 = 2+5+5+5 but I'll let you check that you can't write 1+2+5+7 as the sum of four numbers in {1,2,5,7}, unless of course you take each one once.

%K hard,nonn

%O 1,2

%A Vincent Nesme (vnesme(AT)ens-lyon.fr), May 28 2005