login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers m such that the GCD of the x's that satisfy sigma(x) = m is 4.
5

%I #23 Dec 19 2024 06:16:10

%S 7,210,378,630,1904,3570,6188,6510,7154,9296,9800,10220,12446,13664,

%T 14378,17654,17780,18536,19110,19376,19530,20034,20580,21266,23240,

%U 23310,24150,24584,25298,26754,27930,28938,29106,29610,30380,31640,34146,34230,34664

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

%H Amiram Eldar, <a href="/A241649/b241649.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..698 from Robert Israel)

%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).

%e sigma(104) = sigma(116) = 210, and gcd(104, 116) = 4, hence 210 is in the sequence.

%e Likewise 6510 is obtained with sigma of [2600, 2900, 3464, 3716], with gcd 4.

%p N:= 10^5: # for terms <= N

%p V:= Vector(N):

%p for x from 1 to N do

%p s:= numtheory:-sigma(x);

%p if s <= N then

%p if V[s] = 0 then V[s]:= x

%p else V[s]:= igcd(V[s],x)

%p fi

%p fi

%p od:

%p select(t -> V[t]=4, [$1..N]); # _Robert Israel_, Aug 18 2019

%o (PARI) is(k) = gcd(invsigma(k)) == 4; \\ _Amiram Eldar_, Dec 19 2024, using _Max Alekseyev_'s invphi.gp

%Y Cf. A000203, A240667, A241625, A241646, A241647, A241648, A241650.

%K nonn

%O 1,1

%A _Michel Marcus_, Apr 26 2014