A326148 - OEIS

%I #15 Dec 10 2023 17:51:01

%S 15,91,207,703,847,1023,1891,2701,2725,5551,12403,15043,18721,19359,

%T 38503,49141,79003,88831,104653,146611,148951,188191,218791,226801,

%U 269011,286903,346957,385003,497503,597871,665281,721801,736291,765703,873181,954271,1056331,1207359,1314631,1345873,1373653,1537381,1755001

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

%C 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 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 Of the first 519 terms, 485 are semiprimes.

%H Antti Karttunen, <a href="/A326148/b326148.txt">Table of n, a(n) for n = 1..519; all terms < 2^31</a>

%H <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>

%o (PARI)

%o A020639(n) = if(1==n, n, factor(n)[1, 1]);

%o A326146(n) = (sigma(n)-A020639(n)-n);

%o A326147(n) = gcd(n-A020639(n), sigma(n)-A020639(n)-n);

%o 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 Cf. A020639, A046666, A326064, A326074, A326146, A326147.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jun 10 2019