

A191749


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


0



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
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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



