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A326074 Numbers n for which A326073(n) is equal to abs(1+A326146(n)).

%I A326074 #32 Jun 13 2019 12:51:19
%S A326074 3,6,28,221,391,496,1189,1421,1961,2419,5429,7811,8128,11659,15049,
%T A326074 18871,36581,44461,48689,57721,80851,86519,98431,107869,117739,146171,
%U A326074 169511,181829,207761,235421,240199,280151,312131,387349,437669,497951,525991,637981,685801,735349,752249,804101,885119,950821,1009009
%N A326074 Numbers n for which A326073(n) is equal to abs(1+A326146(n)).
%C A326074 Numbers n such that 1+(A001065(n)-A020639(n)) is not zero and divides 1+n-A020639(n).
%C A326074 Note that whenever n is even, then the above condition reduces to "(even) numbers n such that A048050(n) is not zero and divides n-1", which is a condition satisfied only by the even terms of A000396.
%C A326074 a(375) = 360866239 = 449 * 509 * 1579 is the first term with more than two distinct prime factors, the second is a(392) = 413733139 = 199 * 239 * 8699, and the third is a(485) = 718660177 = 41 * 853 * 20549.
%C A326074 Question: Are any of these terms present also in A326064 and A326148? None of the first 564 terms are. If such intersections are empty, then there are no odd perfect numbers.
%C A326074 If one selects only semiprimes from this sequence, one is left with 6, 221, 391, 1189, 1961, 2419, 5429, 7811, 11659, 15049, 18871, 36581, ... (555 terms out of the first 564 terms). Their smaller prime factors are: 2, 13, 17, 29, 37, 41, 61, 73, 89, 101, 113, 157, 173, 181, 197, 233, 241, 257, 269, 281, 313, ... while their larger prime factors are: 3, 17, 23, 41, 53, 59, 89, 107, 131, 149, 167, 233, 257, 269, 293, 347, 359, 383, 401, 419, 467, 503, 521, ..., and both sequences of primes seem to be monotonic.
%H A326074 Antti Karttunen, <a href="/A326074/b326074.txt">Table of n, a(n) for n = 1..564; all terms < 2^30</a>
%H A326074 <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%o A326074 (PARI)
%o A326074 A020639(n) = if(1==n, n, factor(n)[1, 1]);
%o A326074 A326073(n) = gcd(1+n-A020639(n), 1+sigma(n)-A020639(n)-n);
%o A326074 A326146(n) = (sigma(n)-A020639(n)-n);
%o A326074 isA326074(n) = (A326073(n)==abs(1+A326146(n)));
%Y A326074 Cf. A000203, A001065, A020639, A048050, A061228, A325960, A325961, A326064, A326073, A326146, A326148.
%Y A326074 Cf. A000396 (a subsequence, the even terms of this sequence if there are no odd perfect numbers).
%K A326074 nonn
%O A326074 1,1
%A A326074 _Antti Karttunen_, Jun 10 2019