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
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
KEYWORD
base,nonn
AUTHOR
Tanya Khovanova, Jun 22 2009
EXTENSIONS
Edited by R. J. Mathar, Aug 03 2009
STATUS
approved