A341511 - OEIS

%I #6 Feb 15 2021 22:50:42

%S 1,2,3,3,4,5,4,5,6,9,5,6,9,8,7,6,9,8,7,10,15,7,10,15,12,25,18,11,8,7,

%T 10,15,12,25,16,27,9,8,7,10,15,12,27,18,25,10,15,12,25,18,27,14,11,16,

%U 21,11,14,21,20,35,30,49,24,45,50,13,12,25,18,27,16,11,20,21,14,35,36,45,13,22,33,28,55,42,77,40,63,70,121,60,17

%N Triangular array T(n,k) = A005940(1+A156552(n)+A156552(k)), read by rows, with n >= 1, 1 <= k <= n.

%C A341510 is the main entry for this dyadic function. See comments there.

%H Antti Karttunen, <a href="/A341511/b341511.txt">Table of n, a(n) for n = 1..10440; the first 144 rows of the triangle</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F T(n, k) = A341510(n, k).

%e The triangle begins as:

%e   1,

%e   2,  3,

%e   3,  4,  5,

%e   4,  5,  6,  9,

%e   5,  6,  9,  8,  7,

%e   6,  9,  8,  7, 10, 15,

%e   7, 10, 15, 12, 25, 18, 11,

%e   8,  7, 10, 15, 12, 25, 16, 27,

%e   9,  8,  7, 10, 15, 12, 27, 18, 25,

%e etc.

%o (PARI)

%o up_to = 105;

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o A156552(n) = { my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };

%o A341510sq(n,k) = A005940(1+A156552(n)+A156552(k));

%o A341511list(up_to) = { my(v = vector(up_to), i=0); for(n=1,oo, for(k=1,n, i++; if(i > #v, return(v)); v[i] = A341510sq(n,k))); (v); };

%o v341511 = A341511list(up_to);

%o A341511(n) = v341511[n];

%Y The lower triangular region of A341510 read by rows.

%Y Cf. A005940, A156552.

%Y Cf. A000027 (the left edge), A003961 (the right edge).

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, Feb 15 2021