

A243970


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


1



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, 12, 29, 16, 16, 21, 18, 34, 20, 18, 37, 18, 18, 27, 20, 20, 43, 24, 30, 46, 33, 32, 28, 24, 34, 39, 28, 24, 28, 28, 24, 58, 24, 24, 30, 32, 32, 64, 65, 30, 67, 51
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OFFSET

0,3


COMMENTS

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.


LINKS



EXAMPLE

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.


PROG

(PARI) ps(n) = {vps = []; d = divisors(n); ips = 0; forstep (i=#d, 1, 1, ips += d[i]; vps = concat(vps, ips); ); vps; }
a(n) = {if (n==0, return (1)); i=1; found=0; while (! found, v = ps(i); if (vecsearch(v, n), found=1, i++); ); i; }


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



