OFFSET
1,1
COMMENTS
"composite(n)" stands for "n-th composite number", so composite(1) to composite(8) are 4, 6, 8, 9, 10, 12, 14, 15.
EXAMPLE
composite(1) = 4; (smallest prime factor of 4) = (largest prime factor of 4) = 2. composite(2) = 6, (largest prime factor of 6) = 3. Hence a(1) = 3.
composite(5) = 10; (smallest prime factor of 10) = 2, (largest prime factor of 10) = 5. composite(2) to composite(5) are 6, 8, 9, 10, largest prime factors are 3, 2, 3, 5. Hence a(5) = 3+2+3+5 = 13.
composite(7) = 14; (smallest prime factor of 14) = 2, (largest prime factor of 14) = 7. composite(2) to composite(7) are 6, 8, 9, 10, 12, 14, largest prime factors are 3, 2, 3, 5, 3, 7. Hence a(5) = 3+2+3+5+3+7 = 23.
PROG
(Magma) Composites:=[ j: j in [4..100] | not IsPrime(j) ];
[ &+[ E[ #E] where E is PrimeDivisors(Composites[k]): k in [D[1]..D[ #D]] where D is PrimeDivisors(Composites[n]) ]: n in [1..73] ]; // Klaus Brockhaus, Jun 25 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Jun 16 2009, Jun 18 2009
EXTENSIONS
Edited, corrected (a(39)=33 replaced by 23, a(40)=84 replaced by 89) and extended by Klaus Brockhaus, Jun 25 2009
STATUS
approved