cp's OEIS Frontend

A339492 T(n, k) = tau(k) + floor(n/k) - 1, where tau = A000005. Triangle read by rows.

%I A339492 #17 Dec 31 2020 13:13:22
%S A339492 1,2,2,3,2,2,4,3,2,3,5,3,2,3,2,6,4,3,3,2,4,7,4,3,3,2,4,2,8,5,3,4,2,4,
%T A339492 2,4,9,5,4,4,2,4,2,4,3,10,6,4,4,3,4,2,4,3,4,11,6,4,4,3,4,2,4,3,4,2,12,
%U A339492 7,5,5,3,5,2,4,3,4,2,6,13,7,5,5,3,5,2,4,3,4,2,6,2
%N A339492 T(n, k) = tau(k) + floor(n/k) - 1, where tau = A000005. Triangle read by rows.
%C A339492 A simple path in the divisor graph of {1,...,n} is a sequence of distinct numbers between 1 and n such that if m immediately follows k, then either m divides k or k divides m. Let S(n, k) = divisors(k) union {k*j : j = 2..floor(n/k)}. A path p is only valid if the elements of the path p(k-1) are in S(n, p(k)), for k = 2..n.
%F A339492 T(n, k) = card(divisors(k) union {k*j : j = 2..floor(n/k)}).
%e A339492 Row 6 lists the cardinalities of the sets {1, 2, 3, 4, 5, 6}, {1, 2, 4, 6}, {1, 3, 6}, {1, 2, 4}, {1, 5}, {1, 2, 3, 6}.
%e A339492 The triangle starts:
%e A339492 [1]                       1;
%e A339492 [2]                      2, 2;
%e A339492 [3]                    3, 2, 2;
%e A339492 [4]                   4, 3, 2, 3;
%e A339492 [5]                 5, 3, 2, 3, 2;
%e A339492 [6]                6, 4, 3, 3, 2, 4;
%e A339492 [7]              7, 4, 3, 3, 2, 4, 2;
%e A339492 [8]             8, 5, 3, 4, 2, 4, 2, 4;
%e A339492 [9]           9, 5, 4, 4, 2, 4, 2, 4, 3;
%e A339492 [10]        10, 6, 4, 4, 3, 4, 2, 4, 3, 4.
%p A339492 T := (n, k) -> NumberTheory:-tau(k) + iquo(n, k) - 1:
%p A339492 seq(seq(T(n, k), k = 1..n), n = 1..13);
%Y A339492 T(n, 1) = A000027(n), T(n, n) = A000005(n), T(2n, n) = A334954(n).
%Y A339492 Cf. A339491, A339496, A339489.
%K A339492 nonn,tabl
%O A339492 1,2
%A A339492 _Peter Luschny_, Dec 31 2020