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).

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

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 16 2009, Jun 18 2009

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

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

Extensions

Edited, corrected (a(39)=33 replaced by 23, a(40)=84 replaced by 89) and extended by Klaus Brockhaus, Jun 25 2009