

A161955


TITO2(n): The operation A161594 in binary, digitreversals carried out in base 2.


3



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
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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 nso the base2 representation does not effect 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
T. Khovanova, Turning Numbers Inside Out [From Tanya Khovanova, Jul 07 2009]


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: A325401 A098985 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



