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 A164927 #6 Apr 07 2019 00:01:15
%S A164927 5,5,13,17,5,5,13,29,17,37,5,41,5,13,53,29,61,18,17,73,37,5,41,22,89,
%T A164927 97,5,101,13,53,109,113,29,61,5,18,17,137,34,73,37,149,157,5,41,13,22,
%U A164927 173,89,181,42,193,97,197,5,101,46,13,53,109,30,113,229,29,233,241,61,5,257
%N A164927 Sum of the odd prime divisors of numbers with all odd prime divisors of the form 4k+1.
%C A164927 We define a sequence b(n) = 5, 10, 13, 17, 20, 25, 26, 29, 34, 37, 40, 41, 50, 52, 53, 58, 61, 65, 68, 73, ... to consist of those numbers where all odd prime factors are primes contained in A002144, and which have at least one prime factor in this class.
%C A164927 b(n) differs from A009003 which also contains numbers like 30=2*3*5 or 39=3*13, 3 not being in A002144.
%C A164927 b(n) essentially contains elements of A004613 multiplied by powers of 2.
%C A164927 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 A164927 Sum of distinct Pythagorean prime divisors of integers whose only odd prime divisors are Pythagorean primes A002144.
%C A164927 Analogous sequence for primes of form 4k+3 is A164928.
%C A164927 Analogous sequence for primes of form 6k+1 is A164929.
%C A164927 Analogous sequence for primes of form 6k+5 is A164930.
%e A164927 a(18) = 18 because b(18) = 65 = 5*13, and 5+13 = 18.
%e A164927 The smallest number, all of whose prime factors are of form 4n+1, whose sum of distinct prime factors is prime: 1885 = 5 * 13 * 29; and 5 + 13 + 29 = 47.
%p A164927 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 <> 1 then RETURN(false) ; fi; od: RETURN(true) ; fi; end:
%p A164927 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 A164927 A164927 := proc(n) local f; numtheory[factorset]( b(n)) minus {2} ; add(f,f=%) ; end: seq(A164927(n),n=1..120) ; # _R. J. Mathar_, Sep 09 2009
%Y A164927 Cf. A000040, A002144, A009003, A164927-A164930.
%K A164927 easy,nonn
%O A164927 1,1
%A A164927 _Jonathan Vos Post_, Aug 31 2009
%E A164927 Edited, definition clarified by _R. J. Mathar_, Sep 08 2009