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

1,1

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.

Links

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

Example

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.

Mathematica

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

Crossrefs

Subsequence of A000466, A046642 and A341779.

Cf. A000010, A009191, A268066.

Sequence in context: A364075 A087614 A063739 * A060194 A068858 A280772

Adjacent sequences: A341777 A341778 A341779 * A341781 A341782 A341783

Keyword

nonn

Author

Amiram Eldar, Feb 19 2021

Status

approved