A285330 If n is squarefree, then a(n) = A048675(n), otherwise a(n) = A285328(n).

0, 1, 2, 2, 4, 3, 8, 4, 3, 5, 16, 6, 32, 9, 6, 8, 64, 12, 128, 10, 10, 17, 256, 18, 5, 33, 9, 14, 512, 7, 1024, 16, 18, 65, 12, 24, 2048, 129, 34, 20, 4096, 11, 8192, 22, 15, 257, 16384, 36, 7, 40, 66, 26, 32768, 48, 20, 28, 130, 513, 65536, 30, 131072, 1025, 21, 32, 36, 19, 262144, 34, 258, 13, 524288, 54, 1048576, 2049, 45, 38, 24, 35, 2097152, 50, 27

Offset

1,3

Comments

Each n > 1 occurs exactly twice in this sequence. a(n) tells which number is located at the parent node of the node that contains n in the binary tree A285332. See further comments there.

Links

Antti Karttunen, Table of n, a(n) for n = 1..4096

Formula

If A008683(n) <> 0 [when n is squarefree], a(n) = A048675(n), otherwise a(n) = A285328(n).

Mathematica

Table[Which[n == 1, 0, MoebiusMu@ n != 0, Total@ Map[#2*2^(PrimePi@ #1 - 1) & @@ # &, FactorInteger[n]], True, With[{r = DivisorSum[n, EulerPhi[#] Abs@ MoebiusMu[#] &]}, SelectFirst[Range[n - 2, 2, -1], DivisorSum[#, EulerPhi[#] Abs@ MoebiusMu[#] &] == r &]]], {n, 81}] (* Michael De Vlieger, Dec 31 2018 *)

Prog

(PARI)
A007947(n) = factorback(factorint(n)[, 1]); \\ From Andrew Lelechenko, May 09 2014
A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ Michel Marcus, Oct 10 2016
A285328(n) = { my(r); if((n > 1 && !bitand(n, (n-1))), (n/2), r=A007947(n); if(r==n, 1, n = n-r; while(A007947(n) <> r, n = n-r); n)); };
A285330(n) = if(moebius(n)<>0, A048675(n), A285328(n));
(Scheme) (define (A285330 n) (if (not (zero? (A008683 n))) (A048675 n) (A285328 n)))

Crossrefs

Cf. A008683, A048675, A284584, A285328, A285332, A285333.

Sequence in context: A048675 A162474 A334878 * A048676 A049287 A285620

Adjacent sequences: A285327 A285328 A285329 * A285331 A285332 A285333

Keyword

nonn

Author

Antti Karttunen, Apr 19 2017

Status

approved