A302033 a(n) = A019565(A003188(n)).

1, 2, 6, 3, 15, 30, 10, 5, 35, 70, 210, 105, 21, 42, 14, 7, 77, 154, 462, 231, 1155, 2310, 770, 385, 55, 110, 330, 165, 33, 66, 22, 11, 143, 286, 858, 429, 2145, 4290, 1430, 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

Offset

0,2

Comments

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.

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

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Formula

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

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

a(n+1) = A059897(a(n), A094290(n+1)). - Peter Munn, Apr 01 2019

Mathematica

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

Prog

(PARI)
A003188(n) = bitxor(n, n>>1);
A019565(n) = {my(j); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A302033(n) = A019565(A003188(n));
(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}

Crossrefs

A permutation of A005117. Subsequence of A207901.

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

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

Cf. also A277811, A283475, A284003.

Sequence in context: A121566 A056839 A378679 * A337643 A071301 A145642

Adjacent sequences: A302030 A302031 A302032 * A302034 A302035 A302036

Keyword

nonn,easy

Author

Antti Karttunen & Peter Munn, Apr 16 2018

Status

approved