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.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A164928 Sum of the odd prime divisors of numbers whose odd prime divisors are all of the form 4k+3. 4
3, 3, 7, 3, 11, 3, 7, 3, 19, 10, 11, 23, 3, 3, 7, 31, 14, 3, 19, 10, 43, 11, 23, 47, 3, 7, 3, 7, 22, 59, 31, 10, 14, 67, 26, 71, 3, 19, 18, 79, 3, 83, 10, 43, 11, 23, 34, 47, 3, 7, 14, 103, 107, 3, 7, 22, 59, 11, 31, 10, 127, 46, 131, 14, 26, 67, 26, 139, 50, 71, 3, 10, 151, 19, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
We define a sequence b(n) = 3, 6, 7, 9, 11, 12, 14, 18, 19, 21, 22, 23, ... to consist of those numbers where all odd prime factors are primes contained in A002145, and which have at least one prime factor in this class; b(n) is basically A004144 without the powers of 2.
a(n) is the sum of the distinct odd prime factors of b(n), where "distinct" means that the multiplicity (exponent) in the prime factorization of b(n) is ignored.
Analogous sequence for primes of form 4k+1 is A164927.
Analogous sequence for primes of form 6k+1 is A164929.
Analogous sequence for primes of form 6k+5 is A164930.
LINKS
EXAMPLE
a(11) = 10 because b(11) = 21 = 3*7, and 3+7 = 10.
The smallest nonprime number, all of whose prime factors are of form 4n+3, whose sum of distinct prime factors is prime: b(181) = 3*7*19 = 399; 3+7+19 = 29.
MAPLE
isb := proc(n) fs := numtheory[factorset](n) minus {2} ; if fs = {} then RETURN(false); else for f in fs do if op(1, f) mod 4 <> 3 then RETURN(false) ; fi; od: RETURN(true) ; fi; end:
b := proc(n) if n = 1 then 3; else for a from procname(n-1)+1 do if isb(a) then RETURN(a) ; fi; od: fi; end:
A164928 := proc(n) local f; numtheory[factorset]( b(n)) minus {2} ; add(f, f=%) ; end: seq(A164928(n), n=1..120) ; # R. J. Mathar, Sep 08 2009
MATHEMATICA
sopd[n_]:=Module[{ff=Select[Transpose[FactorInteger[n]][[1]], OddQ]}, If[ And@@ (Mod[#, 4]==3&/@ff), Total[ff], 0]]; Select[Array[sopd, 200], #>0&] (* Harvey P. Dale, Dec 16 2013 *)
CROSSREFS
Sequence in context: A134661 A135434 A204204 * A253249 A069949 A143275
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Aug 31 2009
EXTENSIONS
Edited and extended by R. J. Mathar, Sep 08 2009
STATUS
approved

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 21 14:18 EDT 2024. Contains 372738 sequences. (Running on oeis4.)