This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A164930 #8 Apr 06 2019 23:20:53
%S A164930 5,5,11,17,5,11,23,5,29,17,5,41,11,23,47,5,53,16,29,59,17,71,5,41,83,
%T A164930 22,11,89,23,47,5,101,53,107,16,113,28,29,59,11,5,131,17,137,71,34,
%U A164930 149,5,41,83,167,22,173,11,89,179,23,28,47,191,197,5,101,46,53,107,16,113,227,28
%N A164930 Sum of odd prime divisors of numbers with all odd prime divisors of the form 6k+5.
%C A164930 We define a sequence b(n) = 5, 10, 11, 17, 20, 22, 23, 25, 29, 34, 40, 41, 44, 46, 47, 50, 53, 55, 58, ... to consist of those numbers where all odd prime factors are primes contained in A007528, and which have at least one prime factor in this class. 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.
%C A164930 Analogous sequence for primes of form 4k+1 is A164927.
%C A164930 Analogous sequence for primes of form 4k+3 is A164928.
%C A164930 Analogous sequence for primes of form 6k+1 is A164929.
%C A164930 The sum of an even number of primes of form 6k+1 is even (hence composite).
%C A164930 The sum of 3 primes of form 6n+5 is composite because (6a+5)+(6b+5)+(6c+5) = 3*(a+b+c+3).
%C A164930 However, the sum of 5 primes of form 6n+5 may be prime:
%C A164930 The smallest number, all of whose prime factors are of form 6k+5, whose sum of distinct prime factors is prime: 881705 = 5 * 11 * 17 * 23 * 41, and 5 + 11 + 17 + 23 + 41 = 97 is prime.
%e A164930 a(18) = 16 because b(18)= 55 = 5*11, and 5+11 = 16.
%p A164930 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 6 <> 5 then RETURN(false) ; fi; od: RETURN(true) ; fi; end:
%p A164930 b := proc(n) if n = 1 then 5; else for a from procname(n-1)+1 do if isb(a) then RETURN(a) ; fi; od: fi; end:
%p A164930 A164930 := proc(n) local f; numtheory[factorset]( b(n)) minus {2} ; add(f,f=%) ; end: seq(A164930(n),n=1..120) ; # _R. J. Mathar_, Sep 09 2009
%Y A164930 Cf. A000040, A007528, A164927-A164930.
%K A164930 easy,nonn
%O A164930 1,1
%A A164930 _Jonathan Vos Post_, Aug 31 2009
%E A164930 Edited and extended by _R. J. Mathar_, Sep 09 2009