A243970 - OEIS

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, 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

Table of n, a(n) for n=0..68.

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

Cf. A167485.

Sequence in context: A289507 A076228 A317050 * A282443 A210554 A208912

Adjacent sequences: A243967 A243968 A243969 * A243971 A243972 A243973

KEYWORD

nonn

AUTHOR

Michel Marcus, Jun 16 2014

STATUS

approved