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

1,2

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A008472.

Sequence in context: A202803 A366917 A092185 * A212692 A034134 A081441

Adjacent sequences: A216891 A216892 A216893 * A216895 A216896 A216897

Keyword

nonn

Author

Michel Lagneau, Sep 19 2012

Status

approved