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4 4 25 1296
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By examination I can now produce S(1)..S(8). S(9) may be 36 and, S(10) may be 48 and(S12) may be 72, but being greater than 30 there may be a smaller value with 3 primes.<br>For 3 primes the number of factors is 1+A1+A2+A3+A1*A2+A1+*A3+A2*A3+A1*A2*A3 and are good upto 2*3*5*7 (210). 2*3*5 has 8 factors sobut can not be better than 24. 2**2*3*5=60 and has 12 factors, so it replaces the existing guess (72). This also validates my current guess for 9 and 10. So I can now generate S(1)..S(13).<br>Realizing that the formula for the number of factors for n primes is (1+A1)*(1+A2)...(1+An) I can see why there is no value better than S(n)=2**(n-1) for prime n. I can also calculate S(14):<br>14=(1+6)*(1+1)->2**6*3->192.--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 12:37, 13 April 2019 (UTC)
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