A161955 TITO2(n): The operation A161594 in binary, digit-reversals carried out in base 2.

1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19, 5, 21, 11, 23, 3, 19, 13, 27, 7, 29, 15, 31, 1, 57, 17, 49, 9, 37, 19, 33, 5, 41, 21, 43, 11, 45, 23, 47, 3, 35, 19, 51, 13, 53, 27, 65, 7, 105, 29, 59, 15, 61, 31, 63, 1, 59, 57, 67, 17, 117, 49, 71, 9, 73, 37, 105, 19, 109

Offset

1,3

Comments

The TITO function in binary: Represent n as a product of its prime factors in binary.

Revert the binary digits of each of these factors, then multiply them with the same multiplicities as in n--so the base-2 representation does not affect the exponents in the canonical prime factorization. Reverse the product in binary to get a(n).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..40000

Tanya Khovanova, Turning Numbers Inside Out

Formula

a(n) = A030101(A162742(n)) - R. J. Mathar, Aug 03 2009

Example

To calculate TITO2(n=99): 99 = 3^3*11. Prime factors 3 and 11 in binary are 11 and 1011 correspondingly. Reversing those numbers we get 11 and 1101. The product with multiplicities is the binary product of 11*11*1101 = 1110101. Reversing that we get 1010111, which corresponds to 87. Hence a(99) = 87.

Maple

r:= proc(n) local m, t; m, t:=n, 0; while m>0
      do t:=2*t+irem(m, 2, 'm') od; t end:
a:= n-> r(mul(r(i[1])^i[2], i=ifactors(n)[2])):
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 29 2017

Mathematica

reverseBinPower[{n_, k_}] := FromDigits[Reverse[IntegerDigits[n, 2]], 2]^k fBin[n_] := FromDigits[ Reverse[IntegerDigits[ Times @@ Map[reverseBinPower, FactorInteger[n]], 2]], 2] Table[fBin[n], {n, 200}]

Crossrefs

Cf. A161594.

Sequence in context: A356168 A327539 A072963 * A276234 A000265 A227140

Adjacent sequences: A161952 A161953 A161954 * A161956 A161957 A161958

Keyword

base,nonn

Author

Tanya Khovanova, Jun 22 2009

Extensions

Edited by R. J. Mathar, Aug 03 2009

Status

approved