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A350380 Triangle read by rows in which row n lists A014963(d), the exponential of Mangoldt function, for each divisor d of n.

%I A350380 #16 Dec 29 2021 02:21:26
%S A350380 1,1,2,1,3,1,2,2,1,5,1,2,3,1,1,7,1,2,2,2,1,3,3,1,2,5,1,1,11,1,2,3,2,1,
%T A350380 1,1,13,1,2,7,1,1,3,5,1,1,2,2,2,2,1,17,1,2,3,1,3,1,1,19,1,2,2,5,1,1,1,
%U A350380 3,7,1,1,2,11,1,1,23,1,2,3,2,1,2,1,1,1,5,5,1,2,13,1
%N A350380 Triangle read by rows in which row n lists A014963(d), the exponential of Mangoldt function, for each divisor d of n.
%H A350380 Michel Marcus, <a href="/A350380/b350380.txt">Table of n, a(n) for n = 1..10006</a> (rows 1 to 1358, flattened).
%F A350380 a(n) = A014963(A027750(n)).
%e A350380 Triangle begins:
%e A350380   1;
%e A350380   1, 2;
%e A350380   1, 3;
%e A350380   1, 2, 2;
%e A350380   1, 5;
%e A350380   1, 2, 3, 1;
%e A350380   1, 7;
%e A350380   1, 2, 2, 2;
%e A350380   1, 3, 3;
%e A350380   1, 2, 5, 1;
%e A350380   ...
%t A350380 Table[Exp[MangoldtLambda[Divisors[n]]], {n, 1, 26}] // Flatten (* _Amiram Eldar_, Dec 28 2021 *)
%o A350380 (PARI) M(n) = ispower(n, , &n); if(isprime(n), n, 1); \\ A014963
%o A350380 row(n) = apply(M, divisors(n));
%Y A350380 Cf. A014963, A027750.
%Y A350380 Cf. A000027 (row products), A140255 (row sums).
%K A350380 nonn,tabf
%O A350380 1,3
%A A350380 _Michel Marcus_, Dec 28 2021, following a suggestion from _Charles Kusniec_