This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A347392 #35 Jun 12 2022 09:32:07
%S A347392 8,9,12,13,24,35,160,455,42550,127650,8041950,22469750,58506250,
%T A347392 67409250,175518750,394055550,4246782750
%N A347392 Numbers k such that nearest common ancestor of k and sigma(k) in Doudna tree (A347879) is the grandparent of k.
%C A347392 Note how 13 * 35 = 455.
%C A347392 If there exists any odd perfect numbers x, with sigma(x) = 2x, then 2*x would be a term of this sequence, as then sigma(2*x) = 6*x would be situated as a descendant under the other branch of the grandparent of 2*x (a parent of x), which is m = A064989(x), with m in A005101. Opn x itself would be a term of A336702. Furthermore, if such x is not a multiple of 3 (in which case m is odd and in A005231), then also 3x would be a term of this sequence as sigma(3*x) = 4*sigma(x) = 8*x would be situated as a grandchild of 2x, with 2x being a first cousin of 3x. Also, in that case, 6*x would be located in A336702 (particularly, in A027687) because then sigma(6*x) = 12*sigma(x) = 24*x = 4*(6*x).
%C A347392 .
%C A347392 <--A003961-- m ---(*2)--->
%C A347392 .............../ \...............
%C A347392 / \
%C A347392 / \
%C A347392 / \
%C A347392 x 2m
%C A347392 etc..../ \......2x = sigma(x) 3x....../ \......4m
%C A347392 / \ / \ / \
%C A347392 etc. \ etc. \ etc. etc.
%C A347392 \ \
%C A347392 4x sigma(2x) = 6x
%C A347392 / \ / \
%C A347392 etc \ etc. \
%C A347392 \ \
%C A347392 8x = sigma(3x) 12x
%C A347392 if m odd \
%C A347392 \
%C A347392 24x = sigma(6x) if m odd.
%C A347392 .
%C A347392 Furthermore, if there were any hypothetical odd terms y in A005820 (triperfect numbers), then 2y would be a term of this sequence. See the diagram in A347391.
%C A347392 If it exists, a(18) > 2^33.
%H A347392 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A347392 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A347392 455 is included in the sequence as sigma(455) = 672, and the nearest common ancestor of 455 and 672 in Doudna tree is 42, which is the grandparent of 455 [as 455 = A003961(A003961(42))] and the grand-grand-grand-parent of 672 [as 672 = (2^4)*42].
%o A347392 (PARI) isA347392(n) = (2==A347381(n));
%o A347392 (PARI)
%o A347392 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A347392 A252463(n) = if(!(n%2),n/2,A064989(n));
%o A347392 isA347391(n) = if(1==n,0,my(m=A252463(n), s=sigma(n)); while(s>m, if(s==n, return(0)); s = A252463(s)); (s==m));
%o A347392 isA347391_or_A347392(n) = if(1==n,0,my(m=A252463(A252463(n)), s=sigma(n)); while(s>m, if(s==n, return(0)); s = A252463(s)); (s==m));
%o A347392 isA347392(n) = (isA347391_or_A347392(n) && !isA347391(n));
%Y A347392 Positions of 2's in A347381.
%Y A347392 Cf. A000203, A005101, A005231, A005820, A005940, A027687, A336702, A347391, A347393, A347394, A347879, A348041.
%Y A347392 Cf. also A336834, A353365.
%K A347392 nonn,hard,more
%O A347392 1,1
%A A347392 _Antti Karttunen_, Aug 30 2021