A216894 n - (sum of prime factors of n) is a positive square.

1, 6, 22, 54, 68, 164, 166, 336, 388, 454, 588, 854, 886, 1086, 1122, 1124, 1636, 1710, 1828, 2182, 2356, 2468, 2702, 2960, 3046, 3048, 3708, 3748, 3770, 4036, 4054, 4655, 5106, 5394, 5636, 6502, 7108, 7368, 7956, 8324, 9170, 9188, 9412, 9438, 9471, 9726

Offset: 1

Author

Michel Lagneau, Sep 19 2012

Keywords

• nonn

Comments

Contains 4p for odd prime p if 3p-2 is a square, in particular if p is in A122430. - Robert Israel, Apr 13 2014

Examples

			54 = 2*3^3 and 54 -(2+3) = 49 is a square, hence 54 is in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2121

Crossrefs

Cf. A008472.

Programs

Maple

filter:= proc(x) local y;
    y:= x - add(i, i=numtheory:-factorset(x));
    y > 0 and issqr(y)
end proc;
N:= 10000;  # to get all entries <= N
A216894:= select(filter,[$1..N]); # Robert Israel, Apr 13 2014

Mathematica

nspfQ[n_]:=Module[{c=n-Total[Transpose[FactorInteger[n]][[1]]]},c>0 && IntegerQ[ Sqrt[c]]]; Join[{1},Select[Range[10000],nspfQ]] (* Harvey P. Dale, Feb 12 2015 *)