A191749 Numbers not the sum of a smaller number and its prime factors (with multiplicity).

1, 3, 5, 7, 9, 12, 13, 16, 18, 20, 21, 25, 27, 28, 30, 32, 37, 43, 44, 45, 48, 49, 50, 52, 57, 60, 61, 64, 66, 67, 68, 70, 73, 75, 77, 78, 80, 81, 85, 87, 90, 91, 92, 97, 100, 101, 102, 104, 108, 110, 112, 115, 117, 126

Offset

1,2

Comments

If a number is not squarefree, then its repeated prime factors are added as many times as the exponent indicates (e.g., the sum of prime factors of 8 is 6 since 8 = 2 * 2 * 2 and 2 + 2 + 2 = 6).

No even semiprime (A100484) can be in this sequence, since, if nothing else, it is the sum of a prime number and that prime number's only prime factor (itself).

Links

Table of n, a(n) for n=1..54.

Example

3 is in the sequence since neither 1 + sopfr(1) nor 2 + sopfr(2) add up to 3 (instead these equal 2 and 4 respectively).
Because 2 + sopfr(2) = 4, the number 4 is not in this sequence.

Mathematica

pfAddSeq[start_, max_] := NestWhileList[# + Plus@@Times@@@FactorInteger@# &, start, # < max &]; Complement[Range[200], Flatten[Table[Drop[pfAddSeq[n, 200], 1], {n, 200}]]]

Crossrefs

Cf. A096461, A192896 (only a(1) of those sequences can be in this sequence). Cf. also A001414. Analogous to A005114.

Sequence in context: A131628 A079091 A353149 * A038663 A291154 A246405

Adjacent sequences: A191746 A191747 A191748 * A191750 A191751 A191752

Keyword

nonn

Author

Alonso del Arte, Jul 13 2011

Status

approved