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A216894 n - (sum of prime factors of n) is a positive square. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A216050 A202803 A092185 * A212692 A034134 A081441

Adjacent sequences:  A216891 A216892 A216893 * A216895 A216896 A216897

KEYWORD

nonn

AUTHOR

Michel Lagneau, Sep 19 2012

STATUS

approved

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Last modified June 28 20:39 EDT 2017. Contains 288840 sequences.