

A216213


Numbers n such that sigma*(n) = sum_{k=antidivisors of n} sigma*(k), where sigma*(n) is the sum of the antidivisors of n.


1



1, 2, 11, 12, 15, 16, 22, 31, 76, 152, 309, 1576, 375479, 781314, 1114986, 3734218, 24311881, 68133239, 147881549
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Tested up to n = 108122.
a(20) > 3*10^8.  Donovan Johnson, Mar 22 2013


LINKS

Table of n, a(n) for n=1..19.


EXAMPLE

Antidivisors of 76 are 3, 8, 9, 17 and 51 and their sum is 88.
Antidivisor of 3 is 2 > Sum is 2.
Antidivisors of 8 are 3 and 5 > Sum is 8.
Antidivisors of 9 are 2 and 6 > Sum is 8.
Antidivisors of 17 are 2, 3, 5, 7 and 11 > Sum is 28.
Antidivisors of 51 are 2, 6 and 34 > Sum is 42.
Finally, 2+8+8+28+42=88.


MAPLE

A216213:= proc(q) local a, b, c, j, k, n;
for n from 1 to q do
a:={}; b:=0; for k from 2 to n1 do if abs((n mod k)k/2)<1 then b:=b+k; a:=a union {k}; fi; od;
c:=0; for j from 1 to nops(a) do for k from 2 to a[j]1 do if abs((a[j] mod k)k/2)<1 then c:=c+k; fi; od; od; if b=c then print(n); fi; od; end:
A216213(10^10);


CROSSREFS

Cf. A066272, A178029, A191580, A191581, A192282A192284.
Sequence in context: A175414 A059192 A087339 * A160948 A299973 A136971
Adjacent sequences: A216210 A216211 A216212 * A216214 A216215 A216216


KEYWORD

nonn


AUTHOR

Paolo P. Lava, Mar 13 2013


EXTENSIONS

a(13)a(19) from Donovan Johnson, Mar 22 2013


STATUS

approved



