A390641 Numbers k such that the sum of k and 3 times the sum of its prime factors, counted with multiplicity, is prime.

10, 14, 20, 22, 26, 28, 35, 38, 40, 44, 52, 55, 58, 68, 74, 77, 82, 85, 88, 91, 92, 94, 95, 106, 112, 115, 119, 122, 124, 133, 148, 152, 155, 158, 161, 166, 172, 176, 184, 185, 187, 194, 203, 206, 208, 212, 214, 215, 217, 221, 226, 232, 244, 248, 254, 262, 265, 272, 274, 278, 284, 287, 292, 295

Offset

1,1

Comments

Numbers k such that k + 3*A001414(k) is prime.

Links

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

Example

a(3) = 20 is a term because 20 + 3 * (2 + 2 + 5) = 47 is prime.

Maple

spf:= proc(n) local t; add(t[1]*t[2], t=ifactors(n)[2]) end proc:
select(t -> isprime(t+3*spf(t)), [$1..1000]);

Mathematica

q[n_] := PrimeQ[n + 3 * Plus @@ Times @@@ FactorInteger[n]]; Select[Range[2, 300], q] (* Amiram Eldar, Nov 13 2025 *)

Crossrefs

Cf. A001414, A050703, A390639.

Sequence in context: A251727 A253785 A245729 * A031274 A272375 A395792

Adjacent sequences: A390638 A390639 A390640 * A390642 A390643 A390644

Keyword

nonn

Author

Will Gosnell and Robert Israel, Nov 13 2025

Status

approved