A341780 Starts of runs of 3 consecutive anti-tau numbers (A046642).

3, 15, 195, 255, 483, 783, 1023, 1155, 1295, 1443, 1599, 2703, 3363, 4623, 4899, 5183, 6399, 6723, 7395, 7743, 8463, 8835, 10815, 11235, 11663, 12099, 12543, 15375, 16383, 16899, 17955, 18495, 20163, 24963, 25599, 26895, 27555, 31683, 33855, 35343, 36099, 37635

Offset: 1

Author

Amiram Eldar, Feb 19 2021

Keywords

• nonn

Comments

Since the even anti-tau numbers (A268066) are square numbers, all the terms are of the form 4*k^2 - 1, and there cannot be a run of more than 3 consecutive anti-tau numbers.

Examples

			3 is a term since 3, 4 and 5 are all anti-tau numbers: gcd(3, tau(3)) = gcd(3, 2) = 1, gcd(4, tau(4)) = gcd(4, 3) = 1 and gcd(5, tau(5)) = gcd(5, 2) = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A000466, A046642 and A341779.

Cf. A000010, A009191, A268066.

Programs

Mathematica

antiTauQ[n_] := CoprimeQ[n, DivisorSigma[0, n]]; Select[4*Range[100]^2 - 1, AllTrue[# + {0, 1, 2}, antiTauQ] &]