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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..33.

FORMULA

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

EXAMPLE

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.

MAPLE

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

a:=0; k:=0; while a<n do k:=k+1; a:=a+sigma(n-k)-n+k; od;

if a=n then print(n); fi; od; end: P(10^9);