

A161670


Sum of largest prime factor of composite(k) for k from smallest prime factor of composite(n) to largest prime factor of composite(n).


0



3, 5, 3, 2, 13, 5, 23, 10, 3, 5, 13, 20, 38, 5, 5, 56, 2, 23, 13, 3, 35, 80, 15, 5, 92, 53, 13, 23, 38, 10, 129, 5, 7, 13, 77, 56, 5, 30, 23, 89, 187, 13, 215, 20, 3, 48, 38, 80, 126, 23, 5, 263, 10, 92, 22, 56, 13, 2, 329, 23, 72, 365, 184, 38, 13, 40, 129, 212, 398, 84, 5, 23, 35
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OFFSET

1,1


COMMENTS

"composite(n)" stands for "nth composite number", so composite(1) to composite(8) are 4, 6, 8, 9, 10, 12, 14, 15.


LINKS



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

Cf. A002808 (composite numbers), A111426 (difference between largest and smallest prime factor of composite(n)).


KEYWORD

nonn


AUTHOR



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



