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A286873 Numbers x such that x = Sum_{i=1..k} (x mod d_(x-i)) + Sum_{i=1..k} (x mod d_(x+i)) for some k, where d_(x-i) and d_(x+i) are the aliquot parts of (x-i) and (x+i). 2
7, 10, 16, 27, 75, 87, 109, 120, 151, 1887, 4029, 5829, 17815, 39780, 62485, 238021, 254011, 437744, 779391, 873565, 979389, 1713591, 2409697, 4194303, 4199029, 4607295, 8353791, 9928791, 15370303, 21381096, 33653887, 114203775, 124540389, 2146926591, 6521655540 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Values of k for the listed terms are 2, 2, 2, 2, 2, 1, 1, 3, 1, 1, 1, 1, 1, 3, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, ...

If d_(x-i) were the aliquot parts of (x-i) and d_(x+i) the divisors of (x+i) we would get the average of twin prime pairs (A014574).

If d_(x-i) were the divisors of (x-i) and d_(x+i) the aliquot parts of (x+i) we would get 5, 6, 7, 1296, 3228, 32767, 65784, 128766, 711236, ...

LINKS

Table of n, a(n) for n=1..35.

EXAMPLE

For 7 the value of k is 2. Aliquot parts of 5, 6, 8 and 9 are: [1], [1, 2, 3], [1, 2, 4], [1, 3]. Residues are 0 + 0 + 1 + 1 + 0 + 1 + 3 + 0 + 1 that sum up to 7.

MAPLE

with(numtheory): P:=proc(q) local a, b, c, j, k, n;

for n from 3 to q do a:=0; k:=0; while a<n do k:=k+1;

b:=sort([op(divisors(n+k))]); c:=sort([op(divisors(n-k))]);

a:=a+add(n mod b[j], j=1..nops(b)-1)+add(n mod c[j], j=1..nops(c)-1); od;

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

CROSSREFS

Cf. A014574, A290468, A290469.

Sequence in context: A287567 A301451 A033817 * A218128 A175666 A299997

Adjacent sequences:  A286870 A286871 A286872 * A286874 A286875 A286876

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Aug 02 2017

EXTENSIONS

a(27)-a(35) from Giovanni Resta, Aug 03 2017

STATUS

approved

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Last modified June 4 08:18 EDT 2020. Contains 334825 sequences. (Running on oeis4.)