A316860 Integers k that do not divide A053818(k).

2, 3, 4, 6, 8, 9, 12, 15, 16, 18, 24, 27, 30, 32, 33, 36, 45, 48, 51, 54, 60, 64, 66, 69, 72, 75, 81, 87, 90, 96, 99, 102, 108, 120, 123, 128, 132, 135, 138, 141, 144, 150, 153, 159, 162, 165, 174, 177, 180, 192, 198, 204, 207, 213, 216, 225, 240, 243, 246, 249

Offset: 1

Author

Jianing Song, Jul 15 2018

Keywords

• nonn
• easy

Comments

k is a term iff k = 2^e or k = 3^e*Product_{i=1..s} p_i^e_i, p_i == 2 (mod 3) and e >= 1. If k = 2^e, A053818(k) == (1/2)*k (mod k); if k = 3^e*Product_{i=1..s} p_i^e_i, A053818(k) == (2/3)*k for even s and (1/3)*k for odd s. - Corrected by Robert Israel, Nov 15 2020

Terms < N are getting more and more sparse as N increases. The number of terms below 100, 1000, 10000 and 100000 are 31, 187, 1431 and 12059, respectively.

Examples

			A053818(16) mod 16 = 680 mod 16 = 8 != 0, so 16 is a term.
A053818(33) mod 33 = 7370 mod 33 = 11 != 0, so 33 is a term.
A053818(21) mod 21 = 1806 mod 21 = 0, so 21 is not a term.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..12059 (all terms below 100000)

Crossrefs

Cf. A053818.

Programs

Mathematica

Select[Range@ 250, Function[n, Mod[Total[Select[Range@ n, GCD[#, n] == 1 &]^2], n] != 0]] (* Michael De Vlieger, Jul 19 2018 *)

PARI

pr(n)=my(f=factor(n)[, 1]); prod(i=1, #f, abs(f[i]%3-1));
for(n=2, 1000, if(omega(2*n)==1, print1(n, ", "), if(n%3==0&&pr(n), print1(n, ", "))))