A302033 - OEIS

%I #37 Apr 04 2019 22:43:13

%S 1,2,6,3,15,30,10,5,35,70,210,105,21,42,14,7,77,154,462,231,1155,2310,

%T 770,385,55,110,330,165,33,66,22,11,143,286,858,429,2145,4290,1430,

%U 715,5005,10010,30030,15015,3003,6006,2002,1001,91,182,546,273,1365,2730,910,455,65,130,390,195,39,78,26,13,221,442,1326,663,3315,6630,2210,1105

%N a(n) = A019565(A003188(n)).

%C A squarefree analog of A207901 (and the subsequence consisting of its squarefree terms): Each term is either a divisor or a multiple of the next one, and the terms differ by a single prime factor. Compare also to A284003.

%C For all n >= 0, max(a(n + 1), a(n)) / min(a(n + 1), a(n)) = A094290(n + 1) = prime(valuation(n + 1, 2) + 1) = A000040(A001511(n + 1)). [See _Russ Cox_'s Dec 04 2010 comment in A007814.] - _David A. Corneth_ & _Antti Karttunen_, Apr 16 2018

%H Antti Karttunen, <a href="/A302033/b302033.txt">Table of n, a(n) for n = 0..8191</a>

%F a(n) = A019565(A003188(n)).

%F a(n) = A284003(A064706(n)).

%F a(n+1) = A059897(a(n), A094290(n+1)). - _Peter Munn_, Apr 01 2019

%t Array[Times @@ Prime@ Flatten@ Position[#, 1] &@ Reverse@ IntegerDigits[BitXor[#, Floor[#/2]], 2] &, 72, 0] (* _Michael De Vlieger_, Apr 27 2018 *)

%o (PARI)

%o A003188(n) = bitxor(n, n>>1);

%o A019565(n) = {my(j); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565

%o A302033(n) = A019565(A003188(n));

%o (PARI) first(n) = {my(pr = primes(1 + logint(n, 2)), ex = vector(#pr, i, 1), res = vector(n)); res[1] = 1; for(i = 1, n-1, v = valuation(i, 2); res[i + 1] = res[i] * pr[v++] ^ ex[v]; ex[v]*=-1); res}

%Y A permutation of A005117. Subsequence of A207901.

%Y Cf. A302054 (gives the sum of prime divisors).

%Y Cf. A000040, A001511, A003188, A019565, A034947, A059897, A064706, A094290.

%Y Cf. also A277811, A283475, A284003.

%K nonn,easy

%O 0,2

%A _Antti Karttunen_ & _Peter Munn_, Apr 16 2018