A273992 Numbers whose sum of anti-divisors is equal to the sum of its unitary divisors.

11, 22, 33, 65, 82, 140, 218, 228, 483, 537, 616, 1184, 2889, 6430, 10216, 15849, 21541, 59620, 112590, 117818, 130356, 483153, 3028671, 3589646, 7231219, 8515767, 13050345, 36494625, 44498344, 50414595, 217728002, 459644211, 519061576, 1217532421, 1573368218

Offset

1,1

Links

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

Example

Sum of anti-divisors of 11 is 12. Unitary divisors of 11 are 1, 11 and their sum is 12.

Maple

with(numtheory): P:=proc(q) local a, b, c, j, k, n;
for n from 1 to q do k:=0; j:=n;
while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
c:=ifactors(n)[2]; b:=mul(c[j][1]^c[j][2]+1, j=1..nops(c));
if a=b then print(n); fi; od; end: P(10^6);

Mathematica

Select[Range[5000], Function[n, Total[Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]] == Plus @@ Select[Divisors@ n, GCD[#, n/#] == 1 &]]] (* Michael De Vlieger, Jun 06 2016, after Robert G. Wilson v at A034448 and Harvey P. Dale at A066272 *)

Prog

(PARI) sud(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d));
sad(n) = my(k); if(n>1, k=valuation(n, 2); sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2, 0);
isok(n) = sad(n) == sud(n); \\ Michel Marcus, Jun 12 2016

Crossrefs

Cf. A034448, A066417, A074751, A178029.

Sequence in context: A367339 A065816 A178029 * A283927 A239018 A101145

Adjacent sequences: A273989 A273990 A273991 * A273993 A273994 A273995

Keyword

nonn

Author

Paolo P. Lava, Jun 06 2016

Extensions

a(23)-a(26) from Michel Marcus, Jun 12 2016

a(27)-a(35) from Amiram Eldar, Jul 12 2022

Status

approved