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A302033
a(n) = A019565(A003188(n)).
9
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
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
(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. also A277811, A283475, A284003.
Sequence in context: A372000 A121566 A056839 * A337643 A071301 A145642
KEYWORD
nonn,easy
AUTHOR
STATUS
approved