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A161955 TITO2(n): The operation A161594 in binary, digit-reversals 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 (list; graph; refs; listen; history; text; internal format)
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 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: A244568 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

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Last modified September 22 09:19 EDT 2017. Contains 292336 sequences.