A255217 -id:A255217 - cp's OEIS frontend

A349734 Numbers k such that A255217(k) divides A007504(k).

2, 5, 15, 17, 20, 25, 26, 33, 37, 45, 49, 51, 71, 87, 88, 91, 105, 111, 121, 127, 173, 175, 199, 203, 213, 221, 262, 271, 287, 305, 307, 319, 324, 329, 368, 377, 410, 411, 415, 439, 445, 455, 463, 467, 468, 473, 547, 558, 561, 567, 585, 589, 591, 614, 651, 661, 663, 665, 670, 673, 743, 761, 765

Offset: 1

J. M. Bergot and Robert Israel, Nov 28 2021

nonn

			a(2) = 5 is a term because A255217(5) = 2*3*5*7*11 mod (2+3+5+7+11) = 14 divides 2+3+5+7+11 = 28.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A002110, A007504, A255217, A349738.

P:= 1: S:= 0: p:= 1:
count:= 0: R:= NULL:
for n from 1 while count < 100 do
  p:= nextprime(p);
  P:= P*p; S:= S+p;
  r:= P mod S;
  if r = 0 then next fi;
  v:= S mod r;
  if v = 0 then
    count:= count+1; R:= R,n;
  fi
od:
R;

Select[Range[1000], (m = Mod[Times @@ (p = Prime[Range[#]]), Plus @@ p]) > 0 && Divisible[Plus @@ p, m] &] (* Amiram Eldar, Nov 28 2021 *)

A349738 Numbers k such that A255217(k) divides A002110(k).

Original entry on oeis.org

2, 4, 5, 9, 15, 17, 20, 24, 25, 26, 27, 29, 31, 32, 33, 34, 37, 44, 45, 46, 49, 51, 52, 61, 62, 63, 64, 71, 74, 79, 80, 81, 82, 85, 87, 88, 91, 95, 103, 104, 105, 110, 111, 112, 115, 117, 118, 119, 120, 121, 127, 131, 135, 137, 142, 148, 150, 152, 154, 158, 159, 163, 165, 173, 175, 177, 179, 181

Offset: 1

J. M. Bergot and Robert Israel, Nov 28 2021

nonn

			a(3) = 5 is a term because A255217(5) = 2*3*5*7*11 mod (2+3+5+7+11) = 14 divides 2*3*5*7*11.

Martin Ehrenstein, Table of n, a(n) for n = 1..10000

Cf. A002110, A007504, A255217. Contains A349734.

P:= 1: S:= 0: p:= 1:
count:= 0: R:= NULL:
for n from 1 while count < 100 do
  p:= nextprime(p);
  P:= P*p; S:= S+p;
  r:= P mod S;
  if r = 0 then next fi;
  v:= P mod r;
  if v = 0 then
    count:= count+1; R:= R,n;
  fi
od:
R;

Select[Range[200], (m = Mod[Times @@ (p = Prime[Range[#]]), Plus @@ p]) > 0 && Divisible[Times @@ p, m] &] (* Amiram Eldar, Nov 28 2021 *)

A255383 Compositorial mod sum-of-composites.

Original entry on oeis.org

0, 4, 12, 0, 1, 41, 0, 72, 2, 0, 48, 126, 0, 20, 0, 0, 90, 95, 115, 4, 0, 140, 161, 90, 261, 138, 208, 512, 72, 420, 51, 0, 0, 924, 899, 29, 893, 72, 840, 727, 129, 1185, 194, 732, 1080, 1612, 566, 175, 1352, 1192, 1204, 1360, 428, 957, 2170, 0, 0, 513, 2240

Offset: 1

Walter Carlini, May 14 2015

			For n = 5, a(5) = (4*6*8*9*10) mod (4+6+8+9+10) = 17280 mod 37 = 1.

Cf. A002808, A036691, A053767, A255217.

comp=Select[Range[2,83],!PrimeQ[#]&];Mod[Rest[FoldList[Times,1,comp]],Accumulate[comp]] (* Ivan N. Ianakiev, May 22 2015 *)

a(n) = A036691(n) mod A053767(n).

More terms from Alois P. Heinz, May 21 2015

cp's OEIS Frontend

A349734 Numbers k such that A255217(k) divides A007504(k).

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A349738 Numbers k such that A255217(k) divides A002110(k).

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Maple

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A255383 Compositorial mod sum-of-composites.

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