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A351574 Terms of A228058 missing from A347874.

%I A351574 #11 Aug 22 2025 08:44:46
%S A351574 117,245,333,425,549,605,637,657,725,833,845,873,981,1025,1053,1325,
%T A351574 1413,1421,1445,1629,1737,1805,1813,2009,2057,2061,2169,2225,2493,
%U A351574 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 A351574 Terms of A228058 missing from A347874.
%C A351574 Numbers that satisfy Euler's criterion for the odd perfect numbers (A228058), but do not satisfy the criterion specified in A347874.
%H A351574 Antti Karttunen, <a href="/A351574/b351574.txt">Table of n, a(n) for n = 1..10000</a>
%H A351574 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A351574 (PARI)
%o A351574 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351574 A342926(n) = (A003415(sigma(n))-n);
%o A351574 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 A351574 isA347874(n) = ((n%2)&&!isprime(n)&&!(A342926(n)%2)&&!(A342926(2*n)%3));
%o A351574 isA351574(n) = (isA228058(n) && !isA347874(n));
%Y A351574 Setwise difference A228058 \ A347874, also setwise difference A228058 \ A386429.
%Y A351574 Cf. A000203, A003415.
%K A351574 nonn,changed
%O A351574 1,1
%A A351574 _Antti Karttunen_, Feb 23 2022