cp's OEIS Frontend

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.

A286475 Compound filter (for counting primes of form 6k+1, 6k+2, 6k+3 and 6k+5): a(n) = 6*A032742(n) + (A020639(n) mod 6), a(1) = 1.

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%I A286475 #11 May 12 2017 18:21:37
%S A286475 1,8,9,14,11,20,7,26,21,32,11,38,7,44,33,50,11,56,7,62,45,68,11,74,35,
%T A286475 80,57,86,11,92,7,98,69,104,47,110,7,116,81,122,11,128,7,134,93,140,
%U A286475 11,146,43,152,105,158,11,164,71,170,117,176,11,182,7,188,129,194,83,200,7,206,141,212,11,218,7,224,153,230,67,236,7,242,165,248,11,254,107
%N A286475 Compound filter (for counting primes of form 6k+1, 6k+2, 6k+3 and 6k+5): a(n) = 6*A032742(n) + (A020639(n) mod 6), a(1) = 1.
%H A286475 Antti Karttunen, <a href="/A286475/b286475.txt">Table of n, a(n) for n = 1..10000</a>
%F A286475 a(1) = 1, for n > 1, a(n) = 6*A032742(n) + (A020639(n) mod 6).
%e A286475 For n = 55 = 5*11, a(n) = 6*A032742(55) + (5 modulo 6) = 6*11 + 5 = 71.
%e A286475 For n = 121 = 11*11, a(n) = 6*A032742(121) + (11 modulo 6) = 6*11 + 1 = 71.
%e A286475 For n = 91 = 7*13, a(n) = 6*A032742(91) + (7 modulo 6) = 6*13 + 1 = 79.
%e A286475 For n = 169 = 13*13, a(n) = 6*A032742(169) + (13 modulo 6) = 6*13 + 1 = 79.
%t A286475 With[{k = 6}, Table[Function[{p, d}, k d + Mod[p, k] - k Boole[n == 1]] @@ {#, n/#} &@ FactorInteger[n][[1, 1]], {n, 85}]] (* _Michael De Vlieger_, May 12 2017 *)
%o A286475 (Scheme) (define (A286475 n) (if (= 1 n) n (+ (* 6 (A032742 n)) (modulo (A020639 n) 6))))
%o A286475 (Python)
%o A286475 from sympy import divisors, primefactors
%o A286475 def a(n): return 1 if n==1 else 6*divisors(n)[-2] +(min(primefactors(n))%6) # _Indranil Ghosh_, May 12 2017
%Y A286475 Cf. A020639, A032742, A285729, A286472, A286473, A286474, A286476.
%K A286475 nonn
%O A286475 1,2
%A A286475 _Antti Karttunen_, May 11 2017