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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 (list; graph; refs; listen; history; text; internal format)
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
Cf. A167485.
Sequence in context: A289507 A076228 A317050 * A282443 A210554 A208912
KEYWORD
nonn
AUTHOR
Michel Marcus, Jun 16 2014
STATUS
approved

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Last modified July 13 21:38 EDT 2024. Contains 374288 sequences. (Running on oeis4.)