A241004 Numbers n such that anti-phi(sigma*(n)) = n, where anti-phi is A066452 and sigma* is the sum of anti-divisors of n (A066417).

90, 137, 162, 581, 714, 773, 3735, 4557, 71028

Offset: 1

Author

Paolo P. Lava, Aug 07 2014

Keywords

• nonn
• more

Comments

Like A001229 but using anti-phi(n) (A066452) and sigma*(n) (A066417).

Examples

			90 is in the sequence: Anti-divisors of 90 are 4, 12, 20, 36, 60 and their sum is 132. Anti-phi of 132 is 90.
		

Crossrefs

Cf. A001229, A066417, A066452.

Programs

Maple

isA241004 := proc(n)
    simplify( n = A066452(A066417(n))) ;
end proc:
for n from 1 do
    if isA241004(n) then
        printf("%d\n",n) ;
    end if;
end do: # R. J. Mathar, Aug 07 2014

PARI

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);
antidiv(n) = {my(v = []); for (k=2, n-1, if (abs((n % k) - k/2) < 1, v = concat(v, k));); v;}
antiphi(n) = {my(vad = antidiv(n)); my(nbad = 0); for (j=1, n-1, isad = 1; for (k=1, #vad, if ((j % vad[k]) == 0, isad = 0; break); ); nbad += isad;); nbad;}
isok(n) = n == antiphi(sad(n)); \\ Michel Marcus, Feb 25 2016

Extensions

a(9) from Michel Marcus, Feb 25 2016