A351574 - OEIS

%I #6 Feb 23 2022 21:50:50

%S 117,245,333,425,549,605,637,657,725,833,845,873,981,1025,1053,1325,

%T 1413,1421,1445,1629,1737,1805,1813,2009,2057,2061,2169,2225,2493,

%U 2525,2597,2645,2817,2825,2873,2925,2989,2997,3033,3141,3357,3425,3509,3573,3577,3681,3725,3789,3897,4113,4205,4325,4361,4693,4753

%N Terms of A228058 missing from A347874.

%C Numbers that satisfy Euler's criterion for the odd perfect numbers (A228058), but do not satisfy the criterion specified in A347874.

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A342926(n) = (A003415(sigma(n))-n);

%o isA228058(n) = if(!(n%2)||(omega(n)<2),0,my(f=factor(n),y=0); for(i=1,#f~,if(1==(f[i,2]%4), if((1==y)||(1!=(f[i,1]%4)),return(0),y=1), if(f[i,2]%2, return(0)))); (y));

%o isA347874(n) = ((n%2)&&!isprime(n)&&!(A342926(n)%2)&&!(A342926(2*n)%3));

%o isA351574(n) = (isA228058(n) && !isA347874(n));

%Y Setwise difference A228058 \ A347874.

%Y Cf. A000203, A003415.

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 23 2022