This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A350066 #16 Aug 04 2022 22:28:49
%S A350066 1,2,2,3,3,3,4,5,5,4,5,6,7,6,5,6,7,10,10,7,6,7,10,11,9,11,10,7,8,11,
%T A350066 14,14,14,14,11,8,9,12,13,15,13,15,13,12,9,10,15,20,22,22,22,22,20,15,
%U A350066 10,11,14,21,18,17,21,17,18,21,14,11,12,13,22,25,28,26,26,28,25,22,13,12,13,20,17,21,33,30,19,30,33,21,17,20,13
%N A350066 Symmetric square array A(n,k) = A122111(A122111(n) * A122111(k)), n >= 1, k >= 1, read by antidiagonals.
%C A350066 A122111 is a self-inverse permutation, so this array represents a binary operation A(.,.) over the positive integers that is isomorphic to multiplication. Its primes are the positive powers of 2 (as defined by standard multiplication): 2, 4, 8, 16, 32, ... . The positive powers of 2, as defined by A(.,.), are the prime numbers as we usually understand them: 2, 3, 5, 7, 11, ... . - _Peter Munn_, Aug 04 2022
%H A350066 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A350066 A(n, A061142(n)) = A003961(n). - _Peter Munn_, Aug 04 2022
%e A350066 The top left 15 X 15 corner of the array:
%e A350066 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
%e A350066 2, 3, 5, 6, 7, 10, 11, 12, 15, 14, 13, 20, 17, 22, 21,
%e A350066 3, 5, 7, 10, 11, 14, 13, 20, 21, 22, 17, 28, 19, 26, 33,
%e A350066 4, 6, 10, 9, 14, 15, 22, 18, 25, 21, 26, 30, 34, 33, 35,
%e A350066 5, 7, 11, 14, 13, 22, 17, 28, 33, 26, 19, 44, 23, 34, 39,
%e A350066 6, 10, 14, 15, 22, 21, 26, 30, 35, 33, 34, 42, 38, 39, 55,
%e A350066 7, 11, 13, 22, 17, 26, 19, 44, 39, 34, 23, 52, 29, 38, 51,
%e A350066 8, 12, 20, 18, 28, 30, 44, 27, 50, 42, 52, 45, 68, 66, 70,
%e A350066 9, 15, 21, 25, 33, 35, 39, 50, 49, 55, 51, 70, 57, 65, 77,
%e A350066 10, 14, 22, 21, 26, 33, 34, 42, 55, 39, 38, 66, 46, 51, 65,
%e A350066 11, 13, 17, 26, 19, 34, 23, 52, 51, 38, 29, 68, 31, 46, 57,
%e A350066 12, 20, 28, 30, 44, 42, 52, 45, 70, 66, 68, 63, 76, 78, 110,
%e A350066 13, 17, 19, 34, 23, 38, 29, 68, 57, 46, 31, 76, 37, 58, 69,
%e A350066 14, 22, 26, 33, 34, 39, 38, 66, 65, 51, 46, 78, 58, 57, 85,
%e A350066 15, 21, 33, 35, 39, 55, 51, 70, 77, 65, 57, 110, 69, 85, 91,
%o A350066 (PARI)
%o A350066 up_to = 105;
%o A350066 A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
%o A350066 A350066sq(n,k) = A122111(A122111(n)*A122111(k));
%o A350066 A350066list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A350066sq(col,(a-(col-1))))); (v); };
%o A350066 v350066 = A350066list(up_to);
%o A350066 A350066(n) = v350066[n]; \\ _Antti Karttunen_, Dec 13 2021
%Y A350066 Cf. A122111, A297002 (main diagonal), A253550 (after its initial term, gives row 2 / column 2 from the second term onward).
%Y A350066 See the formula section for the relationships with A003961, A061142.
%Y A350066 Cf. also A003991, A129595, A331590.
%K A350066 nonn,tabl
%O A350066 1,2
%A A350066 _Antti Karttunen_, Dec 13 2021