A241649 Numbers m such that the GCD of the x's that satisfy sigma(x) = m is 4.

7, 210, 378, 630, 1904, 3570, 6188, 6510, 7154, 9296, 9800, 10220, 12446, 13664, 14378, 17654, 17780, 18536, 19110, 19376, 19530, 20034, 20580, 21266, 23240, 23310, 24150, 24584, 25298, 26754, 27930, 28938, 29106, 29610, 30380, 31640, 34146, 34230, 34664

Offset: 1

Author

Michel Marcus, Apr 26 2014

Keywords

• nonn

Examples

			sigma(104) = sigma(116) = 210, and gcd(104, 116) = 4, hence 210 is in the sequence.
Likewise 6510 is obtained with sigma of [2600, 2900, 3464, 3716], with gcd 4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..698 from Robert Israel)
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000203, A240667, A241625, A241646, A241647, A241648, 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]=4, [$1..N]); # Robert Israel, Aug 18 2019

PARI

is(k) = gcd(invsigma(k)) == 4; \\ Amiram Eldar, Dec 19 2024, using Max Alekseyev's invphi.gp