A192282 -id:A192282 - cp's OEIS frontend

A192283 Sum of prime anti-divisors of n = sum of prime anti-divisors of n+1 with n > 1.

237, 4019, 7401, 14178, 14339, 18435, 19146, 21405, 54562, 56348, 60125, 82967, 98447, 99347, 109157, 113391, 125333, 132096, 132386, 145063, 173399, 195213, 260288, 278271, 343848, 384169, 396813, 434375, 460758, 474105, 477707, 528845, 550400, 587211

Offset: 1

Paolo P. Lava, Jul 27 2011

nonn

Like A006145 but using anti-divisors.

			Anti-divisors of 7401 are 2, 6, 19, 41, 113, 131, 361, 779, 4934. The primes are 2, 19, 41, 113 and 131 whose sum is 306.
Anti-divisors of 7402 are 3, 4, 5, 7, 9, 15, 21, 35, 45, 47, 63, 105, 113, 131, 141, 235, 315, 329, 423, 705, 987, 1645, 2115, 2961, 4935. The primes are 3, 5, 7, 47, 113 and 131 whose sum is 306.

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A002961, A006145, A066272, A192282

with(numtheory);
P:=proc(n)
local a,b,i,k;
b:=2;
for i from 4 to n do
  a:=0;
  for k from 2 to i-1 do
    if abs((i mod k)- k/2) < 1 then if isprime(k) then a:=a+k; fi; fi;
  od;
  if a=b then print(i-1); fi;
  b:=a;
od;
end:
P(200000);

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

Original entry on oeis.org

1, 2, 11, 12, 15, 16, 22, 31, 76, 152, 309, 1576, 375479, 781314, 1114986, 3734218, 24311881, 68133239, 147881549

Offset: 1

Paolo P. Lava, Mar 13 2013

nonn

Tested up to k = 108122.

a(20) > 3*10^8. - Donovan Johnson, Mar 22 2013

			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.

Cf. A066272, A178029, A191580, A191581, A192282-A192284.

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);

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

cp's OEIS Frontend

A192283 Sum of prime anti-divisors of n = sum of prime anti-divisors of n+1 with n > 1.

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

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cp's OEIS Frontend

A192283 Sum of prime anti-divisors of n = sum of prime anti-divisors of n+1 with n > 1.

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Maple

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

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Maple

Extensions

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