A339436 -id:A339436 - cp's OEIS frontend

A339437 Numbers k such that A339436(k) is prime.

6, 10, 22, 34, 58, 82, 118, 142, 202, 214, 216, 252, 274, 298, 330, 358, 382, 390, 394, 454, 468, 478, 490, 538, 562, 588, 622, 684, 690, 694, 726, 798, 838, 858, 862, 870, 910, 922, 924, 1042, 1044, 1122, 1138, 1176, 1198, 1210, 1224, 1234, 1254, 1282, 1290, 1318, 1332, 1440, 1482, 1518, 1540

Offset: 1

J. M. Bergot and Robert Israel, Dec 04 2020

nonn

All terms are even.

			a(15)=330 is a member because 330 = 2*3*5*11 and A339436(330) = 2 + 2*3 + 2*3*5 + 3*5*11 + 5*11 + 11 = 269 is prime.

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

Includes A108605. Disjoint from A014612.

Cf. A339436.

A339436:= proc(n) local L,m;
  L:= sort(map(t -> t[1]$t[2],ifactors(n)[2]));
  m:= nops(L);
  add(mul(L[i],i=1..j)+mul(L[i],i=j+1..m),j=1..m-1)
end proc:
select(isprime @ A339436, [seq(i,i=2 .. 10000, 2)]);

A339438 Composite numbers k such that k + A339436(k) is prime.

Original entry on oeis.org

6, 10, 14, 15, 20, 21, 24, 26, 33, 34, 35, 38, 40, 44, 46, 51, 52, 55, 57, 58, 63, 65, 74, 76, 85, 86, 88, 90, 92, 93, 96, 111, 117, 118, 123, 124, 135, 136, 141, 143, 145, 147, 150, 153, 155, 158, 161, 164, 166, 172, 177, 178, 180, 184, 185, 194, 198, 201, 203, 205, 206, 207, 208, 209, 215, 221

Offset: 1

J. M. Bergot and Robert Israel, Dec 04 2020

nonn

If n = p_1 * ... * p_m with primes p_i <= p_{i+1}, then p_1 + p_1*p_2 + ... + p_1*p_2*...*p_m + p2*...*p_m + ... + p_m is prime.

			a(5)=20 is a term because 20=2*2*5 and 2+2*2+2*2*5+2*5+5 = 41 is prime.

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

Includes A088709.

Cf. A339436, A339437.

filter:= proc(n) local L,m;
  L:= sort(map(t -> t[1]$t[2],ifactors(n)[2]));
  m:= nops(L);
  if m=1 then return false fi;
  isprime(n + add(mul(L[i],i=1..j)+mul(L[i],i=j+1..m),j=1..m-1))
end proc:
select(filter, [$4..300]);

cp's OEIS Frontend

A339437 Numbers k such that A339436(k) is prime.

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