

A320021


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


1



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
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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(nk)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: A229862 A302599 A098670 * 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



