A390731 Numbers k not in A000961 such that A001414(k) is in A000961.

6, 10, 12, 14, 15, 18, 20, 22, 24, 28, 34, 39, 40, 45, 46, 48, 52, 54, 55, 56, 58, 63, 66, 75, 76, 80, 82, 87, 88, 90, 92, 94, 96, 98, 99, 104, 108, 117, 118, 136, 140, 142, 147, 148, 152, 153, 158, 165, 168, 171, 172, 175, 176, 183, 184, 189, 198, 200, 202, 207, 210, 214, 224, 225, 240, 245, 247

Offset

1,1

Comments

Numbers k such that k is not a prime power, but the sum of prime factors of k, taken with multiplicity, is a prime power. Here "prime power" includes primes.

Links

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

Example

a(4) = 14 is a term because 14 = 2 * 7 is not a prime power but 2 + 7 = 9 = 3^2 is a prime power.

Maple

filter:= proc(n) local F, t;
   F:= ifactors(n)[2];
   nops(F) > 1 and nops(ifactors(add(t[1]*t[2], t=F))[2]) = 1
end proc:
select(filter, [$1..1000]);

Crossrefs

Cf. A000961, A001414. Includes A108605 and A390729.

Sequence in context: A182301 A069059 A273157 * A139587 A201463 A119313

Adjacent sequences: A390728 A390729 A390730 * A390732 A390733 A390734

Keyword

nonn

Author

Will Gosnell and Robert Israel, Nov 16 2025

Status

approved