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 A164928 #11 Apr 05 2019 05:32:09
%S A164928 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,
%T A164928 22,59,31,10,14,67,26,71,3,19,18,79,3,83,10,43,11,23,34,47,3,7,14,103,
%U A164928 107,3,7,22,59,11,31,10,127,46,131,14,26,67,26,139,50,71,3,10,151,19,18
%N A164928 Sum of the odd prime divisors of numbers whose odd prime divisors are all of the form 4k+3.
%C A164928 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.
%C A164928 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 A164928 Analogous sequence for primes of form 4k+1 is A164927.
%C A164928 Analogous sequence for primes of form 6k+1 is A164929.
%C A164928 Analogous sequence for primes of form 6k+5 is A164930.
%H A164928 Harvey P. Dale, <a href="/A164928/b164928.txt">Table of n, a(n) for n = 1..1000</a>
%e A164928 a(11) = 10 because b(11) = 21 = 3*7, and 3+7 = 10.
%e A164928 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.
%p A164928 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:
%p A164928 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:
%p A164928 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
%t A164928 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 *)
%Y A164928 Cf. A000040, A002145, A009003, A164927-A164930.
%K A164928 easy,nonn
%O A164928 1,1
%A A164928 _Jonathan Vos Post_, Aug 31 2009
%E A164928 Edited and extended by _R. J. Mathar_, Sep 08 2009