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A347413 a(n) = (product of first n semiprimes) mod (sum of first n semiprimes).

%I A347413 #13 Sep 02 2021 05:44:05
%S A347413 0,4,7,14,11,40,17,17,0,8,85,147,62,16,292,26,138,18,0,570,167,257,
%T A347413 360,156,525,882,372,918,0,0,0,0,0,150,0,0,1070,2136,1172,0,1265,1502,
%U A347413 663,0,0,0,0,1208,306,2995,0,1404,1389,636,0,272,0,1944,5216,2268,1548,1160,3300,0,924,84,0,3723
%N A347413 a(n) = (product of first n semiprimes) mod (sum of first n semiprimes).
%C A347413 A surprising number of terms are 0: 3124 of the first 10000 terms.
%H A347413 Robert Israel, <a href="/A347413/b347413.txt">Table of n, a(n) for n = 1..10000</a>
%F A347413 a(n) = A112141(n) mod A062198(n).
%e A347413 The first 3 semiprimes are 4, 6, 9, so a(3) = (4*6*9) mod (4+6+9) = 216 mod 19 = 7.
%p A347413 R:= NULL:
%p A347413 s:= 0: p:= 1: count:= 0:
%p A347413 for n from 4 while count < 100 do
%p A347413   if numtheory:-bigomega(n) = 2 then
%p A347413     count:= count+1: s:= s+n; p:= p*n;
%p A347413     R:= R, p mod s;
%p A347413   fi
%p A347413 od:
%p A347413 R;
%o A347413 (Python)
%o A347413 from sympy import factorint
%o A347413 def aupton(terms):
%o A347413     alst, i, n, s, p = [], 1, 0, 0, 1
%o A347413     while n < terms:
%o A347413         if sum(factorint(i).values()) == 2:
%o A347413             n += 1; s += i; p *= i
%o A347413             alst.append(p%s)
%o A347413         i += 1
%o A347413     return alst
%o A347413 print(aupton(68)) # _Michael S. Branicky_, Sep 01 2021
%Y A347413 Cf. A001358, A062198, A112141, A347421.
%K A347413 nonn
%O A347413 1,2
%A A347413 _J. M. Bergot_ and _Robert Israel_, Aug 31 2021