This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A227478 #10 Sep 16 2017 00:29:06
%S A227478 1146,2874,9870,33220,34353,43140,50694,52290,66440,86280,94350,
%T A227478 100804,101097,103059,106140,121540,125070,127897,132880,139908,
%U A227478 156870,172560,183475,191140,193410,201608,208692,212280,243080,248378,265760,276094,279816,303291
%N A227478 Numbers k such that both the sum of the semiprime divisors of k and the sum of the prime divisors of k are squares.
%C A227478 The sequence is infinite: if a number of the form p(1) * p(2) * ... * p(i)^2 * p(i+1) * ... * p(m) is in the sequence where p(1), ..., p(m) are primes, then the numbers p(1) * p(2) * ... * p(i)^q * p(i+1) * ... * p(m) are also in the sequence for q = 3, 4, ... For example, the infinite subsequence 33220, 66440, 132880, ... contains the numbers of the form 2^q * 5 * 11 * 151 for q = 2, 3, 4, ... where 2+5+11+151 = 169 = 13^2 and 2*2 + 2*5 + 2*11 + 2*151 + 5*11 + 5*151 + 11*151 = 2809 = 53^2.
%C A227478 In this sequence, the corresponding pairs of squares are (961, 196), (2401, 484), (900, 64), (2809, 169), (4900, 361), (7225, 729), (2304, 100), (1521, 100), (2809, 169), (7225, 729), (1225, 64), (3721, 121), (12100, 289), (4900, 361), (2704, 100), (7225, 169), (8100, 400), (2916, 169), (2809, 169), (12769, 225), (1521, 100), (7225, 729), (8464, 225), (13225, 529), (5329, 121), (3721, 121), (1369, 64), (2704, 100), (7225, 169), (13689, 289), (2809, 169), (3364, 100), (12769, 225), (12100, 289), ...
%e A227478 1146 = 2*3*191 is in the sequence because the divisors are {1, 2, 3, 6, 191, 382, 573, 1146}, so the sum of the semiprime divisors is 6 + 382 + 573 = 961 = 31^2 and the sum of the prime divisors is 2 + 3 + 191 = 196 = 14^2.
%p A227478 with(numtheory):for n from 2 to 310000 do:x:=divisors(n):n1:=nops(x): y:=factorset(n):n2:=nops(y):s1:=0:s2:=0:for i from 1 to n1 do: if bigomega(x[i])=2 then s1:=s1+x[i]:else fi:od: s2:=sum('y[i]', 'i'=1..n2):if sqrt(s1)=floor(sqrt(s1)) and sqrt(s2)=floor(sqrt(s2)) then printf(`%d, `,n):else fi:od:
%t A227478 Rest@ Select[Range[3*10^5], AllTrue[{DivisorSum[#, # &, PrimeOmega@ # == 2 &], DivisorSum[#, # &, PrimeQ]}, IntegerQ@ Sqrt@ # &] &] (* _Michael De Vlieger_, Sep 15 2017 *)
%Y A227478 Cf. A001358, A008472, A076920, A164722, A227476.
%K A227478 nonn
%O A227478 1,1
%A A227478 _Michel Lagneau_, Jul 13 2013