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Numbers k such that k and k+1 are both anti-tau numbers (A046642).
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%I #9 Feb 20 2021 04:28:05

%S 3,4,15,16,64,100,195,196,255,256,483,484,676,783,784,1023,1024,1155,

%T 1156,1295,1296,1443,1444,1599,1600,1936,2116,2703,2704,3363,3364,

%U 3844,4096,4623,4624,4899,4900,5183,5184,5476,5776,6399,6400,6723,6724,7395,7396

%N Numbers k such that k and k+1 are both anti-tau numbers (A046642).

%C Since the even anti-tau numbers (A268066) are square numbers, all the terms are either of the form 4*k^2 - 1 or 4*k^2.

%H Amiram Eldar, <a href="/A341779/b341779.txt">Table of n, a(n) for n = 1..10000</a>

%e 3 is a term since 3 and 4 are both anti-tau numbers: gcd(3, tau(3)) = gcd(3, 2) = 1 and gcd(4, tau(4)) = gcd(4, 3) = 1.

%t antiTauQ[n_] := CoprimeQ[n, DivisorSigma[0, n]]; s = {}; Do[k = 4*n^2; If[antiTauQ[k], If[antiTauQ[k - 1], AppendTo[s, k - 1]]; If[antiTauQ[k + 1], AppendTo[s, k]]], {n, 1, 50}]; s

%Y Subsequence of A046642 and A081350.

%Y Cf. A000010, A009191, A114617, A268066, A341780.

%K nonn

%O 1,1

%A _Amiram Eldar_, Feb 19 2021