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

1,1

Comments

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

Links

Table of n, a(n) for n=1..73.

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)).

Sequence in context: A205009 A101778 A292570 * A135514 A251754 A225581

Adjacent sequences: A161667 A161668 A161669 * A161671 A161672 A161673

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