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

1,1

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.

Links

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

Example

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.

Mathematica

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

Prog

(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, ", "))))

Crossrefs

Cf. A053818.

Sequence in context: A331827 A231404 A364291 * A097273 A006446 A261342

Adjacent sequences: A316857 A316858 A316859 * A316861 A316862 A316863

Keyword

nonn,easy

Author

Jianing Song, Jul 15 2018

Status

approved