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

0, 4, 7, 14, 11, 40, 17, 17, 0, 8, 85, 147, 62, 16, 292, 26, 138, 18, 0, 570, 167, 257, 360, 156, 525, 882, 372, 918, 0, 0, 0, 0, 0, 150, 0, 0, 1070, 2136, 1172, 0, 1265, 1502, 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

Offset: 1

Author

J. M. Bergot and Robert Israel, Aug 31 2021

Keywords

• nonn

Comments

A surprising number of terms are 0: 3124 of the first 10000 terms.

Examples

			The first 3 semiprimes are 4, 6, 9, so a(3) = (4*6*9) mod (4+6+9) = 216 mod 19 = 7.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A062198, A112141, A347421.

Programs

Maple

R:= NULL:
s:= 0: p:= 1: count:= 0:
for n from 4 while count < 100 do
  if numtheory:-bigomega(n) = 2 then
    count:= count+1: s:= s+n; p:= p*n;
    R:= R, p mod s;
  fi
od:
R;

Python

from sympy import factorint
def aupton(terms):
    alst, i, n, s, p = [], 1, 0, 0, 1
    while n < terms:
        if sum(factorint(i).values()) == 2:
            n += 1; s += i; p *= i
            alst.append(p%s)
        i += 1
    return alst
print(aupton(68)) # Michael S. Branicky, Sep 01 2021

Formula

a(n) = A112141(n) mod A062198(n).