cp's OEIS Frontend

A194196 Numbers k such that the sum of the divisors of k and the sum of the distinct prime divisors of k are both a square.

%I A194196 #23 Dec 05 2020 04:53:39
%S A194196 1,66,94,1092,1146,1416,1491,1782,2130,2159,2805,3012,3531,4836,8736,
%T A194196 9065,9911,12532,13156,15960,16194,24096,25866,27652,29316,29484,
%U A194196 30942,34162,34782,34860,37736,37884,38232,38688,40257,41331,48204,51460,54162,54411
%N A194196 Numbers k such that the sum of the divisors of k and the sum of the distinct prime divisors of k are both a square.
%H A194196 Amiram Eldar, <a href="/A194196/b194196.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Donovan Johnson)
%F A194196 {A006532 intersection A164722}.
%e A194196 94 is in the sequence because the distinct prime divisors are {2,47} -> sum = 7^2, and the divisors are {1,2,47,94} -> sum = 12^2.
%p A194196 isA006532 :=proc(n) issqr(numtheory[sigma](n)) ; end proc:
%p A194196 A008472 := proc(n) add(d, d=numtheory[factorset](n)) ; end proc:
%p A194196 isA164722 :=proc(n) issqr(A008472(n)) ; end proc:
%p A194196 for n from 1 to 50000 do if isA006532(n) and isA164722(n) then printf("%d,",n); end if; end do; # _R. J. Mathar_, Aug 18 2011
%o A194196 (PARI) isok(k) = my(f=factor(k)); issquare(sigma(f)) && issquare(vecsum(f[,1])); \\ _Michel Marcus_, Dec 05 2020
%Y A194196 Cf. A000203, A006532, A008472, A164722.
%K A194196 nonn
%O A194196 1,2
%A A194196 _Michel Lagneau_, Aug 18 2011