The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

%I #7 Sep 08 2022 08:45:45

%S 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,

%T 23,38,10,129,5,7,13,77,56,5,30,23,89,187,13,215,20,3,48,38,80,126,23,

%U 5,263,10,92,22,56,13,2,329,23,72,365,184,38,13,40,129,212,398,84,5,23,35

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

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

%e 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.

%e 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.

%e 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.

%o (Magma) Composites:=[ j: j in [4..100] | not IsPrime(j) ];

%o [ &+[ 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

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

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Jun 16 2009, Jun 18 2009

%E Edited, corrected (a(39)=33 replaced by 23, a(40)=84 replaced by 89) and extended by _Klaus Brockhaus_, Jun 25 2009

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 23 07:28 EDT 2024. Contains 372760 sequences. (Running on oeis4.)