A241647 Numbers m such that the GCD of the x's that satisfy sigma(x) = m is 2.

3, 126, 186, 399, 924, 1350, 1386, 1530, 1806, 2106, 2646, 2652, 2814, 2916, 3066, 3150, 3654, 3870, 4662, 4914, 6162, 6426, 6846, 6882, 6930, 7098, 7566, 7620, 8190, 8910, 9270, 10842, 11076, 12222, 12870, 14586, 14910, 15210, 15246, 15930, 16506, 17010

Offset: 1

Author

Michel Marcus, Apr 26 2014

Keywords

• nonn

Examples

			We have sigma(68) = sigma(82) = 126, and gcd(68, 82) = 2, hence 126 is in the sequence.
On the other hand, for x in [20, 26, 41], sigma(x) = 42, and gcd(20, 26, 41) = 1, hence 42 is not here, although gcd(20, 26) is 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1849 from Robert Israel)
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000203, A240667, A241625, A241646, A241647, A241648, A241649, A241650.

Programs

Maple

N:= 10^5: # for terms <= N
V:= Vector(N):
for x from 1 to N do
  s:= numtheory:-sigma(x);
  if s <= N then
    if V[s] = 0 then V[s]:= x
    else V[s]:= igcd(V[s], x)
    fi
  fi
od: select(t -> V[t]=2, [$1..N]); # Robert Israel, Aug 18 2019

PARI

is(k) = gcd(invsigma(k)) == 2; \\ Amiram Eldar, Dec 19 2024, using Max Alekseyev's invphi.gp