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 A164929 #9 Apr 07 2019 00:01:22
%S A164929 7,13,7,19,13,7,31,37,19,43,7,13,7,61,31,67,73,37,19,79,43,20,97,7,
%T A164929 103,13,109,7,61,31,127,26,67,139,73,37,151,19,157,79,163,13,43,181,
%U A164929 20,193,97,7,199,103,13,211,38,109,223,7,229,241,61,32,31,127,44,26,67,271,277
%N A164929 Sum of odd prime divisors of numbers with all odd prime divisors of the form 6k+1.
%C A164929 We define a sequence b(n) = 7, 13, 14, 19, 26, 28, 31, 37, 38, 43, 49, 52, ... to consist of those numbers where all odd prime factors are primes contained in A002476, and which have at least one prime factor in this class; b(n) is basically elements of A004611 multiplied by powers of 2.
%C A164929 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 A164929 Analogous sequence for primes of form 4k+1 is A164927.
%C A164929 Analogous sequence for primes of form 4k+3 is A164928.
%C A164929 Analogous sequence for primes of form 6k+5 is A164930.
%C A164929 The sum of an even number of primes of form 6n+1 is even (hence composite).
%C A164929 The sum of 3 primes of form 6k+1 is composite because (6a+1)+(6b+1)+(6c+1) = 3*(a+b+c+1). However (see 2nd example) the sum of 5 primes of form 6k+1 may be prime.
%e A164929 a(22) = 20 because b(22) = 91 = 7*13, and 7+13 = 20.
%e A164929 The smallest number, all of whose prime factors are of form 6k+1, whose sum of distinct prime factors is prime: 1983163 = 7 * 13 * 19 * 31 * 37, and 7 + 13 + 19 + 31 + 37 = 107 is prime.
%p A164929 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 <> 1 then RETURN(false) ; fi; od: RETURN(true) ; fi; end:
%p A164929 b := proc(n) if n = 1 then 7; else for a from procname(n-1)+1 do if isb(a) then RETURN(a) ; fi; od: fi; end:
%p A164929 A164929 := proc(n) local f; numtheory[factorset]( b(n)) minus {2} ; add(f,f=%) ; end: seq(A164929(n),n=1..120) ; # _R. J. Mathar_, Sep 09 2009
%Y A164929 Cf. A000040, A002476, A164927-A164930.
%K A164929 easy,nonn
%O A164929 1,1
%A A164929 _Jonathan Vos Post_, Aug 31 2009
%E A164929 Edited and extended by _R. J. Mathar_, Sep 09 2009