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Smallest positive integer m such that n can be expressed as a partial sum of the divisors of m taken in decreasing order.
1

%I #9 Jun 22 2014 02:13:27

%S 1,1,2,2,3,5,4,4,7,6,10,6,6,9,8,8,16,10,10,19,15,14,12,14,14,12,26,12,

%T 12,29,16,16,21,18,34,20,18,37,18,18,27,20,20,43,24,30,46,33,32,28,24,

%U 34,39,28,24,28,28,24,58,24,24,30,32,32,64,65,30,67,51

%N Smallest positive integer m such that n can be expressed as a partial sum of the divisors of m taken in decreasing order.

%C Sequence is similar to A167485, but here, the partial sums are evaluated in decreasing order starting from the highest divisor of n, n, down to the smallest one, 1. Thus for any n>0, a(n) exists and is at most equal to n: the highest divisor of n.

%e From n=1 to 2, these partial sums are: 1; 2, 3. So 3 has appeared in the partial divisors sums of 2. Hence a(3)=2.

%o (PARI) ps(n) = {vps = []; d = divisors(n); ips = 0; forstep (i=#d, 1, -1, ips += d[i]; vps = concat(vps, ips);); vps;}

%o a(n) = {if (n==0, return (1)); i=1; found=0; while (! found, v = ps(i); if (vecsearch(v, n), found=1, i++);); i;}

%Y Cf. A167485.

%K nonn

%O 0,3

%A _Michel Marcus_, Jun 16 2014