A341059 -id:A341059 - cp's OEIS frontend

A341061 Numbers k such that A340179(k) is prime.

5, 28, 44, 51, 58, 61, 63, 90, 93, 108, 129, 136, 145, 148, 186, 208, 234, 235, 241, 247, 262, 272, 277, 278, 300, 306, 310, 314, 316, 321, 329, 335, 379, 384, 386, 414, 428, 446, 448, 449, 475, 480, 492, 514, 535, 537, 546, 548, 572, 580, 599, 609, 611, 616, 618, 626, 660, 670, 673, 680, 683

Offset: 1

J. M. Bergot and Robert Israel, Feb 04 2021

nonn

			a(3) = 44 is a term because A340179(44) = 211 is prime.

Robert Israel, Table of n, a(n) for n = 1..3000

Cf. A340179, A341059, A341060.

f:= proc(n) local C, s, c;
  C:=select(t -> igcd(t, n) = 1, [$1..n-1]);
  s:= convert(C, `+`);
  add(s mod c, c = C)
end proc:
select(t -> isprime(f(t)), [$1..1000]);

A341060 Numbers k such that A340179(k) is a multiple of k.

Original entry on oeis.org

1, 2, 10, 16, 30, 74, 81, 97, 489, 525, 607, 1861, 4439, 26051

Offset: 1

J. M. Bergot and Robert Israel, Feb 04 2021

			a(4) = 16 is a term because A340179(16) = 32 = 2*16.

Cf. A340179, A341059, A341061.

f:= proc(n) local C, s, c;
  C:=select(t -> igcd(t, n) = 1, [$1..n-1]);
  s:= convert(C, `+`);
  add(s mod c, c = C)
end proc:
select(t -> f(t) mod t = 0, [$1..5000]);

A340179[n_] := Total@Mod[#2, #1]& @@ {#, Total@#}& @ Select[Range[n], GCD[#, n] == 1&];
Reap[For[k = 1, k <= 80000, k++, If[Divisible[A340179[k], k], Print[k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, May 16 2023, after Michael De Vlieger in A340179 *)

cp's OEIS Frontend

A341061 Numbers k such that A340179(k) is prime.

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