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

1,1

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);

Mathematica

ok[n_] := Block[{s=0, k=n}, While[k>0 && s<n, k--; s += DivisorSigma[1, k] - k]; s == n]; Select[Range[10^5], ok] (* Giovanni Resta, Oct 09 2018 *)

Crossrefs

Cf. A001065, A320022.

Sequence in context: A302599 A098670 A343570 * A081407 A268857 A205857

Adjacent sequences: A320018 A320019 A320020 * A320022 A320023 A320024

Keyword

nonn,more

Author

Paolo P. Lava, Oct 03 2018

Extensions

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

Status

approved