A320021 Numbers equal to the sum of the aliquot parts of the previous k numbers, for some k.

5, 6, 7, 8, 35, 40, 51, 237, 263, 264, 280, 387, 899, 1300, 7300, 8363, 8364, 11764, 26740, 26939, 46595, 59004, 80877, 131580, 5244549, 5462385, 17062317, 75097524, 127838820, 323987589, 1162300835, 1381439877, 4943600220

Offset: 1

Author

Paolo P. Lava, Oct 03 2018

Keywords

• nonn
• more

Comments

So far 2 <= k <= 4 (k = 2 for 7, 35, 51, 237, 263, 387, 899, 8363, 26939, 46595, 80877, ...; k = 3 for 5, 8, 40, 264, 280, 1300, 7300, 8364, 11764, 26740, 59004, 131580, ...; k = 4 for 6). Are there terms with k = 5, 6, 7, ...?

a(34) > 10^12. - Giovanni Resta, Oct 09 2018

If we were looking at numbers equal to the sum of the aliquot parts of the previous k numbers and of the following k, for some k, the first terms would be 2263024 and 128508838576.

Examples

			5 is in the sequence because aliquot parts of 4 are 1, 2, of 3 is 1, of 2 is 1: 1 + 2 + 1 + 1 = 5.
6 is in the sequence because aliquot parts of 5 is 1, of 4 are 1, 2, of 3 is 1, of 2 is 1: 1 + 1 + 2 + 1 + 1 = 6.
7 is in the sequence because aliquot parts of 6 are 1, 2, 3, of 5 is 1: 1 + 2 + 3 + 1 = 7.
		

Crossrefs

Cf. A001065, A320022.

Programs

Maple

with(numtheory): P:=proc(q) local a,j,k,n; for n from 1 to q do
a:=0; k:=0; while a
				

Mathematica

ok[n_] := Block[{s=0, k=n}, While[k>0 && sGiovanni Resta, Oct 09 2018 *)

Formula

a(n) = Sum_{i = 1..k} A001065(a(n)-i), for some k.

Extensions

a(25)-a(33) from Giovanni Resta, Oct 09 2018