A243971 Numbers n that cannot be obtained as a partial sum of the divisors (taken in descending order, from m down to 1) of any m < n.

1, 2, 5, 10, 16, 19, 26, 29, 34, 37, 43, 46, 58, 64, 65, 67, 73, 82, 86, 94, 101, 109, 122, 130, 134, 142, 145, 146, 149, 157, 163, 190, 193, 197, 199, 202, 206, 211, 229, 257, 262, 281, 283, 290, 298, 302, 310, 334, 337, 347, 349, 367, 401, 409, 421, 430

Offset

1,2

Comments

Numbers such that A243970(n) = n.

Is this sequence infinite? - Franklin T. Adams-Watters, Jul 20 2017

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

From n=1 to 4, these partial sums are: 1; 2, 3; 3, 4; 4, 6, 7. So it is not possible to obtain 5 with any partial sum of divisors of numbers that are less than 5. And indeed A243970(5) is equal to 5. Hence 5 is in this sequence.

Mathematica

Module[{nn = 432, s}, s = Array[Function[d, Array[Total@ Take[d, -#] &, Length@ d]]@ Divisors@ # &, nn - 1]; Select[Range@ nn, ! MemberQ[Flatten@ Take[s, # - 1], #] &]] (* Michael De Vlieger, Jul 22 2017 *)

Crossrefs

Cf. A243970.

Sequence in context: A064513 A117582 A002134 * A062472 A135061 A323624

Adjacent sequences: A243968 A243969 A243970 * A243972 A243973 A243974

Keyword

nonn

Author

Michel Marcus, Jun 16 2014

Status

approved