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A216213 Numbers n such that sigma*(n) = sum_{k=anti-divisors of n} sigma*(k), where sigma*(n) is the sum of the anti-divisors 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

Anti-divisors of 76 are 3, 8, 9, 17 and 51 and their sum is 88.

Anti-divisor of 3 is 2 -> Sum is 2.

Anti-divisors of 8 are 3 and 5 -> Sum is 8.

Anti-divisors of 9 are 2 and 6 -> Sum is 8.

Anti-divisors of 17 are 2, 3, 5, 7 and 11 -> Sum is 28.

Anti-divisors 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 n-1 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, A192282-A192284.

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

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Last modified August 23 00:50 EDT 2019. Contains 326211 sequences. (Running on oeis4.)