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%I #14 Apr 15 2023 01:49:30
%S 2,3,11,35,71,191,419,659,1091,1199,1379,1655,2015,2135,2339,2591,
%T 3059,4439,6119,6215,6335,7055,8099,8351,8519,9815,11159,12419,12431,
%U 12599,12719,12851,13679,15119,15239,16415,16919,17255,17879,18215,18479
%N Numbers k such that A055079(k) = 2^k.
%H Ray Chandler, <a href="/A057838/b057838.txt">Table of n, a(n) for n = 1..13925</a>
%F 2^a(n) = A057841(n) = A055079(a(n)).
%F A001221(A055079(a(n))) = 1.
%e 11 is a term: 2^11 has 11 nonprime divisors; c(11)=A055079(11) could not have r = 2, 3, 4 or more distinct prime divisors because 11 + {2, 3, 4, 5, 6, 7, 8, 9, ...} values of corresponding d(c(11)) = {13, 14, 15, ...} had 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2 non-distinct prime divisors, which provides an upper bound for r ... in contradiction with demanded values: 2, 3, 4, 5, 6, 7, ... This is why A055079(11)=2048. Larger cases are handled in a similar way.
%e a(35) = 15239 since A055079(15239) = 2^15239, which has 4588 decimal digits.
%e A protocol for 15239 is as follows: u=15239; t0=Table[s, {s, 0, 17}]; t1=Table[mr[w], {w, u, u+17}]; t2=t1-t0; g=Table[{w, mr[w]}, {w, u, u+17}]; i1=TimeUsed[]; Write["a(bad)tx1", u, t1, t2, g]; 15239.
%e Supposed number of A001221(x) which should be larger or equal than A001222(d(x)): {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}.
%e A001222(d(x)) {3, 6, 1, 2, 2, 4, 2, 6, 2, 5, 4, 5, 2, 5, 2, 3, 5, 4}.
%e A001222(d(x)) - A001221(x) (negative value means "nasty case") {3, 5, -1, -1, -2, -1, -4, -1, -6, -4, -6, -6, -10, -8, -12, -12, -11, -13} numbers (corresponding d(x) values for some x) together with A001222[d(x)] {{15239, 3}, {15240, 6}, {15241, 1}, {15242, 2}, {15243, 2}, {15244, 4}, {15245, 2}, {15246, 6}, {15247, 2}, {15248, 5}, {15249, 4}, {15250, 5}, {15251, 2}, {15252, 5}, {15253, 2}, {15254, 3}, {15255, 5}, {15256, 4}}.
%Y Cf. A055079, A001221, A001222, A000005, A058060, A058061, A057841.
%K nonn
%O 1,1
%A _Labos Elemer_, Nov 24 2000
%E Edited, corrected and extended by _Ray Chandler_, Aug 14 2010
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