cp's OEIS Frontend

A326148 Odd numbers > 1, not powers of primes, for which A326147(n) is equal to abs(A326146(n)).

%I A326148 #15 Dec 10 2023 17:51:01
%S A326148 15,91,207,703,847,1023,1891,2701,2725,5551,12403,15043,18721,19359,
%T A326148 38503,49141,79003,88831,104653,146611,148951,188191,218791,226801,
%U A326148 269011,286903,346957,385003,497503,597871,665281,721801,736291,765703,873181,954271,1056331,1207359,1314631,1345873,1373653,1537381,1755001
%N A326148 Odd numbers > 1, not powers of primes, for which A326147(n) is equal to abs(A326146(n)).
%C A326148 Odd numbers > 1, not powers of primes, for which A326146(n) [= (sigma(n)-A020639(n)-n)] is not zero and divides n-A020639(n).
%C A326148 Question: Are any of these terms present also in A326064 and A326074? None of the first 519 terms are. If such intersections are empty, then there are no odd perfect numbers.
%C A326148 Of the first 519 terms, 485 are semiprimes.
%H A326148 Antti Karttunen, <a href="/A326148/b326148.txt">Table of n, a(n) for n = 1..519; all terms < 2^31</a>
%H A326148 <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%o A326148 (PARI)
%o A326148 A020639(n) = if(1==n, n, factor(n)[1, 1]);
%o A326148 A326146(n) = (sigma(n)-A020639(n)-n);
%o A326148 A326147(n) = gcd(n-A020639(n), sigma(n)-A020639(n)-n);
%o A326148 isA326148(n) = if((n>1)&&(n%2)&&!isprimepower(n), my(s=factor(n)[1, 1], t=n-s, u=sigma(n)-s-n); (u && !(t%u)), 0);
%Y A326148 Cf. A020639, A046666, A326064, A326074, A326146, A326147.
%K A326148 nonn
%O A326148 1,1
%A A326148 _Antti Karttunen_, Jun 10 2019