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 A322482 Table read by downward antidiagonals: T(n,k) is the greatest divisor of n which is a unitary divisor of k. 1
 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 2, 5, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 6, 1, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 7, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS This relation was defined by Cohen in 1960. The common notation for T(n,k) is (n,k)*. If T(n,k) = 1 then n is said to be semi-prime to k. In general T(n,k) != T(k,n). The relation is used to define semi-unitary divisors (A322483). REFERENCES J. Sandor and B. Crstici, Handbook of Number Theory, II, Springer Verlag, 2004, chapter 3.6, pp. 281. LINKS Eckford Cohen, Arithmetical functions associated with the unitary divisors of an integer, Mathematische Zeitschrift, Vol. 74, No. 1 (1960), pp. 66-80. M. V. Subbarao On some arithmetic convolutions, The theory of arithmetic functions, Springer, Berlin, Heidelberg, 1972, pp. 247-271. D. Suryanarayana and V. Siva Rama Prasad, Sum functions of k-ary and semi-k-ary divisors, Journal of the Australian Mathematical Society, Vol. 15, No. 2 (1973), pp. 148-162. FORMULA T(1,n) = T(n,1) = 1. T(n,n) = n. EXAMPLE The table starts   1  1  1  1  1  1  1  1  1  1 ...   1  2  1  1  1  2  1  1  1  2 ...   1  1  3  1  1  3  1  1  1  1 ...   1  2  1  4  1  2  1  1  1  2 ...   1  1  1  1  5  1  1  1  1  5 ...   1  2  3  1  1  6  1  1  1  2 ...   1  1  1  1  1  1  7  1  1  1 ...   1  2  1  4  1  2  1  8  1  2 ...   1  1  3  1  1  3  1  1  9  1 ...   1  2  1  1  5  2  1  1  1 10 ...   ... The triangle formed by the antidiagonals starts   1   1 1   1 2 1   1 1 1 1   1 1 3 2 1   1 1 1 1 1 1   1 2 1 4 1 2 1   1 1 3 1 1 3 1 1   1 1 1 2 5 1 1 2 1   ... MATHEMATICA udiv[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; semiuGCD[a_, b_] := Max[ Intersection[Divisors[a], udiv[b]]]; Table[semiuGCD[n, k], {n, 1, 20}, {k, n-1, 1, -1 }] // Flatten PROG (PARI) udivisors(n) = {my(d=divisors(n)); select(x->(gcd(x, n/x)==1), d); } T(n, k) = {my(dn = divisors(n), udk = udivisors(k)); vecmax(setintersect(dn, udk)); } \\ Michel Marcus, Dec 14 2018 CROSSREFS Cf. A050873 (gcd), A165430 (unitary gcd). Sequence in context: A205617 A204112 A186027 * A231071 A209156 A329325 Adjacent sequences:  A322479 A322480 A322481 * A322483 A322484 A322485 KEYWORD nonn,tabl AUTHOR Amiram Eldar, Dec 11 2018 STATUS approved

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Last modified August 1 15:44 EDT 2021. Contains 346393 sequences. (Running on oeis4.)