A241648 Numbers m such that the GCD of the x's that satisfy sigma(x) = m is 3.

4, 124, 320, 392, 416, 800, 1352, 1520, 2912, 2960, 3536, 3872, 5720, 5936, 6320, 7112, 8216, 9176, 9912, 10472, 11816, 12152, 12896, 13280, 14960, 15176, 16080, 16400, 16536, 18032, 18392, 18560, 19136, 19880, 20000, 21632, 21680, 21920, 22736, 23120, 23816

Offset: 1

Author

Michel Marcus, Apr 26 2014

Keywords

• nonn

Examples

			We have sigma(48) = sigma(75) = 124, and gcd(48, 75) = 3, hence 124 is in the sequence.
Likewise, we have sigma(x) = 2912 for x = [1116, 1236, 1701, 2007, 2181], with gcd 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..850 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]=3, [$1..N]); # Robert Israel, Aug 18 2019

PARI

is(k) = gcd(invsigma(k)) == 3; \\ Amiram Eldar, Dec 19 2024, using Max Alekseyev's invphi.gp