cp's OEIS Frontend

A325979 Odd numbers k for which gcd(A325977(k), A325978(k)) is equal to abs(A325978(k)).

%I A325979 #24 Jul 21 2025 00:00:53
%S A325979 1,3465,72981,78651,80937,152703,199341,201771,241605,253287,492507,
%T A325979 631881,880821,933147,985473,1063755,1209285,1244133,1292445,1313235,
%U A325979 1327095,1347885,1360881,1451835,1521135,1597365,1620375,1814373,2015475,2664585,6058233,6676371,8186751,11119761,17496243,18379935,28695627
%N A325979 Odd numbers k for which gcd(A325977(k), A325978(k)) is equal to abs(A325978(k)).
%C A325979 Provided that A325977(k) and A325978(k) are never zero for the same k, these are odd numbers k such that A325978(k) is not zero and divides A325977(k).
%C A325979 Of the first 281 terms, only a(5) = 80937, a(51) = 86086881, a(175) = 43024468437, and a(262) = 564858541521 are in A228058. - Updated Jul 20 2025
%H A325979 Giovanni Resta, <a href="/A325979/b325979.txt">Table of n, a(n) for n = 1..281</a> (terms < 10^12; first 65 terms from Antti Karttunen)
%H A325979 <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>.
%o A325979 (PARI)
%o A325979 A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
%o A325979 A034460(n) = (A034448(n) - n);
%o A325979 A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o A325979 A325313(n) = (A048250(n) - n);
%o A325979 A325977(n) = ((A034460(n)+A325313(n))/2);
%o A325979 A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
%o A325979 A325314(n) = (n - A162296(n));
%o A325979 A048146(n) = (sigma(n)-A034448(n));
%o A325979 A325814(n) = (n-A048146(n));
%o A325979 A325978(n) = ((A325314(n)+A325814(n))/2);
%o A325979 A325975(n) = gcd(A325977(n), A325978(n));
%o A325979 isA325979(n) = ((n%2)&&(A325975(n)==abs(A325978(n))));
%o A325979 \\ Or alternatively as:
%o A325979 isA325979(n) = if(!(n%2),0,my(x = A325977(n), y = A325978(n)); (!x&&!y)||(y&&!(x%y)));
%Y A325979 Cf. A228058, A325975, A325977, A325978, A325981.
%K A325979 nonn
%O A325979 1,2
%A A325979 _Antti Karttunen_, Jun 02 2019