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A216894 n - (sum of prime factors of n) is a positive square. 1

%I #19 Feb 12 2015 15:10:25

%S 1,6,22,54,68,164,166,336,388,454,588,854,886,1086,1122,1124,1636,

%T 1710,1828,2182,2356,2468,2702,2960,3046,3048,3708,3748,3770,4036,

%U 4054,4655,5106,5394,5636,6502,7108,7368,7956,8324,9170,9188,9412,9438,9471,9726

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

%C Contains 4p for odd prime p if 3p-2 is a square, in particular if p is in A122430. - _Robert Israel_, Apr 13 2014

%H Robert Israel, <a href="/A216894/b216894.txt">Table of n, a(n) for n = 1..2121</a>

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

%p filter:= proc(x) local y;

%p y:= x - add(i, i=numtheory:-factorset(x));

%p y > 0 and issqr(y)

%p end proc;

%p N:= 10000; # to get all entries <= N

%p A216894:= select(filter,[$1..N]); # _Robert Israel_, Apr 13 2014

%t 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 *)

%Y Cf. A008472.

%K nonn

%O 1,2

%A _Michel Lagneau_, Sep 19 2012

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)