A074253 Numbers n such that the sum of squarefree numbers from the smallest prime factor of n to the largest prime factor of n is a square.

1, 111, 159, 299, 323, 333, 477, 555, 777, 793, 795, 913, 922, 999, 1113, 1221, 1431, 1443, 1665, 1749, 1844, 1887, 2067, 2109, 2331, 2385, 2553, 2703, 2766, 2775, 2867, 2993, 2997, 3021, 3219, 3339, 3441, 3657, 3663, 3688, 3885, 3887, 3975, 4107, 4293

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..2657

Example

111 = 3*37 and the sum of squarefree numbers between 3 and 37 is 3 + 5 + 6 + 7 + 10 + 11 + 13 + 14 + 15 + 17 + 19 + 21 + 22 + 23 + 26 + 29 + 30 + 31 + 33 + 34 + 35 + 37 = 441, a square.

Maple

N:= 10^4: # to get all terms <= N
sf:= select(numtheory:-issqrfree, [$1..N]):
ssf:= ListTools:-PartialSums(sf):
filter:= proc(n) local r, i, j;
   r:= numtheory:-factorset(n);
   j:= ListTools:-BinarySearch(sf, max(r));
   i:= ListTools:-BinarySearch(sf, min(r));
   issqr(ssf[j] - ssf[i-1])
end proc:
filter(1):= true:
select(filter, [$1..N]); # Robert Israel, Jan 31 2018

Mathematica

Select[Range[5000], IntegerQ@ Sqrt@ Total@ Select[Range[First@ #, Last@ #], SquareFreeQ] &[FactorInteger[#][[All, 1]]] &] (* Michael De Vlieger, Jan 31 2018 *)

Crossrefs

Sequence in context: A108721 A084325 A234803 * A245385 A245364 A172189

Adjacent sequences: A074250 A074251 A074252 * A074254 A074255 A074256

Keyword

nonn

Author

Jason Earls, Sep 20 2002

Status

approved