OFFSET
1,1
COMMENTS
Note how 13 * 35 = 455.
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).
.
<--A003961-- m ---(*2)--->
.............../ \...............
/ \
/ \
/ \
x 2m
etc..../ \......2x = sigma(x) 3x....../ \......4m
/ \ / \ / \
etc. \ etc. \ etc. etc.
\ \
4x sigma(2x) = 6x
/ \ / \
etc \ etc. \
\ \
8x = sigma(3x) 12x
if m odd \
\
24x = sigma(6x) if m odd.
.
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.
If it exists, a(18) > 2^33.
LINKS
EXAMPLE
PROG
(PARI) isA347392(n) = (2==A347381(n));
(PARI)
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)};
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));
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));
isA347392(n) = (isA347391_or_A347392(n) && !isA347391(n));
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Antti Karttunen, Aug 30 2021
STATUS
approved