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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 Adjacent sequences:  A243967 A243968 A243969 * A243971 A243972 A243973 KEYWORD nonn AUTHOR Michel Marcus, Jun 16 2014 STATUS approved

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Last modified December 8 04:31 EST 2019. Contains 329850 sequences. (Running on oeis4.)