A265646 Numbers k such that k = Sum_{i=1..j} (d_i mod d), where d_i are their aliquot parts and d is one of them.

24, 84, 120, 270, 672, 1080, 1170, 1488, 1638, 2160, 3360, 3960, 5400, 7392, 10920, 13104, 22932, 24384, 30240, 32640, 64260, 167580, 199584, 241920, 290160, 293760, 333312, 351000, 411264, 435708, 445536, 510720, 523776, 524160, 594048, 725400, 760320, 804384

Offset

1,1

Comments

All terms are multiples of 6.

The sequence is a subset of A273124.

Links

Table of n, a(n) for n=1..38.

Paolo P. Lava, First 50 terms and their value of d

Example

Aliquot parts of 24 are 1, 2, 3, 4, 6, 8, 12 and 1 mod 12 + 2 mod 12 + 3 mod 12 + 4 mod 12 + 6 mod 12 + 8 mod 12 + 12 mod 12 = 1 + 2 + 3 + 4 + 6 + 8 + 0 = 24.
Aliquot parts of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60. In this case we can choose two different values: 24 and 30. In fact the sum of divisors from 1 to 20 is 86. Then 24 mod 24 = 0, 30 mod 24 = 6, 40 mod 24 = 16, 60 mod 24 = 12 and 86 + 0 + 6 + 16 + 12 = 120. Again, 24 mod 30 = 24, 30 mod 30 = 0, 40 mod 30 = 10, 60 mod 30 = 0 and 86 + 24 + 0 + 10 + 0 = 120.

Maple

with(numtheory): P:= proc(q) local a, b, j, k, n;
for n from 1 to q do a:=sort([op(divisors(n))]);
for k from 1 to nops(a)-1 do b:=0; for j from 1 to nops(a)-1 do b:=b+(a[j] mod a[k]); od;
if b=n then print(n); break; fi; od; od; end: P(10^9);

Mathematica

Select[6 Range[10^5], MemberQ[Function[d, Total@ Mod[d, #] & /@ d]@ Most@ Divisors@ #, #] &] (* Michael De Vlieger, May 17 2016 *)

Crossrefs

Cf. A273124.

Sequence in context: A182915 A030622 A063456 * A304158 A045946 A192838

Adjacent sequences: A265643 A265644 A265645 * A265647 A265648 A265649

Keyword

nonn,easy

Author

Paolo P. Lava, May 17 2016

Status

approved