A074253 - OEIS

%I #13 Feb 01 2018 02:52:40

%S 1,111,159,299,323,333,477,555,777,793,795,913,922,999,1113,1221,1431,

%T 1443,1665,1749,1844,1887,2067,2109,2331,2385,2553,2703,2766,2775,

%U 2867,2993,2997,3021,3219,3339,3441,3657,3663,3688,3885,3887,3975,4107,4293

%N 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.

%H Robert Israel, <a href="/A074253/b074253.txt">Table of n, a(n) for n = 1..2657</a>

%e 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.

%p N:= 10^4: # to get all terms <= N

%p sf:= select(numtheory:-issqrfree,[$1..N]):

%p ssf:= ListTools:-PartialSums(sf):

%p filter:= proc(n) local r,i,j;

%p    r:= numtheory:-factorset(n);

%p    j:= ListTools:-BinarySearch(sf, max(r));

%p    i:= ListTools:-BinarySearch(sf, min(r));

%p    issqr(ssf[j] - ssf[i-1])

%p end proc:

%p filter(1):= true:

%p select(filter, [$1..N]); # _Robert Israel_, Jan 31 2018

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

%K nonn

%O 1,2

%A _Jason Earls_, Sep 20 2002