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 A379010 #9 Dec 14 2024 11:01:08
%S A379010 1,2,2,2,6,4,4,8,20,6,4,18,24,42,10,4,12,100,60,110,12,6,24,40,294,
%T A379010 120,156,16,8,20,120,72,1210,192,272,18,6,54,48,420,160,2028,288,342,
%U A379010 22,8,40,500,96,1320,216,4624,396,506,28,10,36,168,2058,180,2496,352,6498,616,812,30,8,24,200,660,13310,264,4896,504,11638,840,930,36
%N A379010 Square array A(n, k) = phi(A246278(n, k)), read by falling antidiagonals; Euler totient function applied to the prime shift array.
%C A379010 Each column is strictly increasing.
%H A379010 Antti Karttunen, <a href="/A379010/b379010.txt">Table of n, a(n) for n = 1..11325; the first 150 antidiagonals, flattened</a>
%H A379010 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%e A379010 The top left corner of the array:
%e A379010 k= | 1 2 3 4 5 6 7 8 9 10
%e A379010 2k= | 2 4 6 8 10 12 14 16 18 20
%e A379010 ----+-------------------------------------------------------------------
%e A379010 1 | 1, 2, 2, 4, 4, 4, 6, 8, 6, 8,
%e A379010 2 | 2, 6, 8, 18, 12, 24, 20, 54, 40, 36,
%e A379010 3 | 4, 20, 24, 100, 40, 120, 48, 500, 168, 200,
%e A379010 4 | 6, 42, 60, 294, 72, 420, 96, 2058, 660, 504,
%e A379010 5 | 10, 110, 120, 1210, 160, 1320, 180, 13310, 1560, 1760,
%e A379010 6 | 12, 156, 192, 2028, 216, 2496, 264, 26364, 3264, 2808,
%e A379010 7 | 16, 272, 288, 4624, 352, 4896, 448, 78608, 5472, 5984,
%e A379010 8 | 18, 342, 396, 6498, 504, 7524, 540, 123462, 9108, 9576,
%e A379010 9 | 22, 506, 616, 11638, 660, 14168, 792, 267674, 17864, 15180,
%e A379010 10 | 28, 812, 840, 23548, 1008, 24360, 1120, 682892, 26040, 29232,
%e A379010 11 | 30, 930, 1080, 28830, 1200, 33480, 1260, 893730, 39960, 37200,
%e A379010 12 | 36, 1332, 1440, 49284, 1512, 53280, 1656, 1823508, 59040, 55944,
%o A379010 (PARI)
%o A379010 up_to = 11325; \\ = binomial(150+1,2)
%o A379010 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 A379010 A379010sq(row,col) = eulerphi(A246278sq(row,col));
%o A379010 A379010list(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] = A379010sq(col,(a-(col-1))))); (v); };
%o A379010 v379010 = A379010list(up_to);
%o A379010 A379010(n) = v379010[n];
%Y A379010 Cf. A000010, A246278, A379011.
%Y A379010 Cf. A062570 (row 1), A006093 (column 1), A036689 (column 2), A083553 (column 3), A135177 (column 4).
%K A379010 nonn,tabl
%O A379010 1,2
%A A379010 _Antti Karttunen_, Dec 14 2024