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 A341608 #12 Dec 22 2024 20:04:09
%S A341608 1,2,1,0,2,1,3,1,2,1,1,3,2,2,1,1,2,3,2,2,1,1,2,2,3,2,2,1,4,1,3,1,3,2,
%T A341608 2,1,2,4,2,3,2,3,2,2,1,2,3,4,2,3,2,3,2,2,1,1,3,3,4,2,3,2,3,2,2,1,1,2,
%U A341608 3,2,4,2,3,2,3,2,2,1,1,2,2,2,3,4,2,3,2,3,2,2,1,0,1,4,2,3,3,4,2,3,2,3,2,2,1
%N A341608 Square array A(n,k) = A341524(A246278(n,k)), read by falling antidiagonals; number of prime factors (with mult.) in the denominator of abundancy index as applied onto prime shift array A246278.
%H A341608 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A341608 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A341608 A(n,k) = A001222(A341606(n,k)) = A001222(A017666(A246278(n,k))).
%e A341608 The top left corner of the array:
%e A341608 n= 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
%e A341608 2n= 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42
%e A341608 -----+---------------------------------------------------------------
%e A341608 1 | 1, 2, 0, 3, 1, 1, 1, 4, 2, 2, 1, 1, 1, 0, 1, 5, 1, 4, 1, 2, 1,
%e A341608 2 | 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 2, 1, 2, 2, 5, 2, 4, 1, 4, 2,
%e A341608 3 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 1, 3, 3, 5, 2, 4, 1, 4, 2,
%e A341608 4 | 1, 2, 2, 3,*1, 3, 2, 4,*2,*2, 2, 4, 2, 3,*2, 5, 2,*3, 2,*3, 3,
%e A341608 5 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2,*2, 3, 5, 2, 4, 2, 4, 3,
%e A341608 6 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2,*3, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 7 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 8 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3,*1, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 9 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 10 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 11 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2,*3, 2, 3, 3, 5, 2, 4,*1, 4, 3,
%e A341608 12 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 13 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 14 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 15 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2,*2, 3, 5, 2, 4, 2, 4, 3,
%e A341608 16 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 17 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 18 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 19 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 20 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 21 | 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 2, 4, 2, 3, 3, 5, 2, 4, 2, 4, 3,
%e A341608 etc.
%e A341608 Positions where columns are not monotonic (i.e., with sudden drops) are marked with an asterisk (*). See the example section of A341606 for their further elaboration.
%o A341608 (PARI)
%o A341608 up_to = 105;
%o A341608 A246278sq(row,col) = if(1==row,2*col, my(f = factor(2*col)); for(i=1, #f~, f[i,1] = prime(primepi(f[i,1])+(row-1))); factorback(f));
%o A341608 A017666(n) = denominator(sigma(n)/n);
%o A341608 A341608sq(row,col) = bigomega(A017666(A246278sq(row,col)));
%o A341608 A341608list(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] = A341608sq(col,(a-(col-1))))); (v); };
%o A341608 v341608 = A341608list(up_to);
%o A341608 A341608(n) = v341608[n];
%Y A341608 Cf. A001222, A017666, A341606, A341607, A341628.
%Y A341608 Sequence A341524 applied to prime shift array A246278.
%K A341608 nonn,tabl
%O A341608 1,2
%A A341608 _Antti Karttunen_, Feb 16 2021