Geodesic
On the functional equation $F(mn)F((m,n))=F(m)F(n)f((m,n))$
Portugaliae mathematica, Tome 26 (1967) no. 1, pp. 101-107.

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Keywords: number theory 
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     author = {Chidambaraswamy, J.},
     title = {On the functional equation $F(mn)F((m,n))=F(m)F(n)f((m,n))$},
     journal = {Portugaliae mathematica},
     pages = {101--107},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {1967},
     mrnumber = {0248097},
     zbl = {0189.04302},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PORMA_1967__26_1_115007/}
}
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Chidambaraswamy, J. On the functional equation $F(mn)F((m,n))=F(m)F(n)f((m,n))$. Portugaliae mathematica, Tome 26 (1967) no. 1, pp. 101-107. http://geodesic.mathdoc.fr/item/PORMA_1967__26_1_115007/