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A316860 Integers k that do not divide A053818(k). 2
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 (list; graph; refs; listen; history; text; internal format)
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). If k = 2^e, A053818(k) == (1/2)*k (mod n); if n = 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.

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: A122380 A033501 A231404 * A097273 A006446 A261342

Adjacent sequences:  A316857 A316858 A316859 * A316861 A316862 A316863

KEYWORD

nonn,easy

AUTHOR

Jianing Song, Jul 15 2018

STATUS

approved

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Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)