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Triangle read by rows in which row n lists A014963(d), the exponential of Mangoldt function, for each divisor d of n.
1

%I #16 Dec 29 2021 02:21:26

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

%H Michel Marcus, <a href="/A350380/b350380.txt">Table of n, a(n) for n = 1..10006</a> (rows 1 to 1358, flattened).

%F a(n) = A014963(A027750(n)).

%e Triangle begins:

%e 1;

%e 1, 2;

%e 1, 3;

%e 1, 2, 2;

%e 1, 5;

%e 1, 2, 3, 1;

%e 1, 7;

%e 1, 2, 2, 2;

%e 1, 3, 3;

%e 1, 2, 5, 1;

%e ...

%t Table[Exp[MangoldtLambda[Divisors[n]]], {n, 1, 26}] // Flatten (* _Amiram Eldar_, Dec 28 2021 *)

%o (PARI) M(n) = ispower(n, , &n); if(isprime(n), n, 1); \\ A014963

%o row(n) = apply(M, divisors(n));

%Y Cf. A014963, A027750.

%Y Cf. A000027 (row products), A140255 (row sums).

%K nonn,tabf

%O 1,3

%A _Michel Marcus_, Dec 28 2021, following a suggestion from _Charles Kusniec_