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A341511 Triangular array T(n,k) = A005940(1+A156552(n)+A156552(k)), read by rows, with n >= 1, 1 <= k <= n.

%I A341511 #6 Feb 15 2021 22:50:42
%S A341511 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 A341511 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 A341511 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 A341511 Triangular array T(n,k) = A005940(1+A156552(n)+A156552(k)), read by rows, with n >= 1, 1 <= k <= n.
%C A341511 A341510 is the main entry for this dyadic function. See comments there.
%H A341511 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 A341511 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A341511 T(n, k) = A341510(n, k).
%e A341511 The triangle begins as:
%e A341511   1,
%e A341511   2,  3,
%e A341511   3,  4,  5,
%e A341511   4,  5,  6,  9,
%e A341511   5,  6,  9,  8,  7,
%e A341511   6,  9,  8,  7, 10, 15,
%e A341511   7, 10, 15, 12, 25, 18, 11,
%e A341511   8,  7, 10, 15, 12, 25, 16, 27,
%e A341511   9,  8,  7, 10, 15, 12, 27, 18, 25,
%e A341511 etc.
%o A341511 (PARI)
%o A341511 up_to = 105;
%o A341511 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A341511 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 A341511 A341510sq(n,k) = A005940(1+A156552(n)+A156552(k));
%o A341511 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 A341511 v341511 = A341511list(up_to);
%o A341511 A341511(n) = v341511[n];
%Y A341511 The lower triangular region of A341510 read by rows.
%Y A341511 Cf. A005940, A156552.
%Y A341511 Cf. A000027 (the left edge), A003961 (the right edge).
%K A341511 nonn,tabl
%O A341511 1,2
%A A341511 _Antti Karttunen_, Feb 15 2021