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Square array where the row n lists all nonnegative numbers k for which A328578(k) = n, read by falling antidiagonals.
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%I #12 Oct 27 2019 17:31:59

%S 1,3,0,5,12,2,7,24,6,4,9,30,18,8,10,11,42,34,16,14,20,13,54,36,32,38,

%T 22,28,15,60,48,64,58,26,50,82,17,72,66,152,62,40,52,88,116,19,84,78,

%U 184,112,44,56,106,118,148,21,90,96,210,166,46,74,110,140,178,208,23,102,108,242,176,68,76,128,142,196,412,418

%N Square array where the row n lists all nonnegative numbers k for which A328578(k) = n, read by falling antidiagonals.

%C Array is read by descending antidiagonals with (n,k) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ... where A(n,k) is the k-th solution x to A328578(x) = n.

%H Antti Karttunen, <a href="/A328631/b328631.txt">Table of n, a(n) for n = 1..1081; the first 46 antidiagonals of the array</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%e The top left 12 X 12 corner of the array:

%e n +------------------------------------------------------

%e 1 | 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ...

%e 2 | 0, 12, 24, 30, 42, 54, 60, 72, 84, 90, ...

%e 3 | 2, 6, 18, 34, 36, 48, 66, 78, 96, 108, ...

%e 4 | 4, 8, 16, 32, 64, 152, 184, 210, 242, 274, ...

%e 5 | 10, 14, 38, 58, 62, 112, 166, 176, 214, 218, ...

%e 6 | 20, 22, 26, 40, 44, 46, 68, 70, 86, 92, ...

%e 7 | 28, 50, 52, 56, 74, 76, 80, 94, 98, 100, ...

%e 8 | 82, 88, 106, 110, 128, 130, 134, 158, 182, 262, ...

%e 9 | 116, 118, 140, 142, 146, 160, 164, 170, 188, 190, ...

%e 10 | 148, 178, 196, 200, 202, 206, 328, 352, 374, 376, ...

%e 11 | 208, 412, 416, 562, 568, 586, 590, 592, 596, 614, ...

%e 12 | 418, 598, 626, 628, 778, 800, 802, 826, 830, 832, ...

%o (PARI)

%o up_to = 78;

%o A257993(n) = { for(i=1,oo,if(n%prime(i),return(i))); }

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A328578(n) = A257993(A276086(A276086(n)));

%o memoA328631sq = Map();

%o A328631sq(n, k) = { my(v=0); if(!mapisdefined(memoA328631sq,[n,k-1],&v),if(1==k, v=-1, v = A328631sq(n, k-1))); for(i=1+v,oo,if(A328578(i)==n,mapput(memoA328631sq,[n,k],i); return(i))); };

%o A328631list(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] = A328631sq(col,(a-(col-1))))); (v); };

%o v328631 = A328631list(up_to);

%o A328631(n) = v328631[n];

%Y Rows 1-6: A005408, A328632, A328633, A328634, A328635, A328636.

%Y Column 1: A328761.

%Y Cf. A257993, A276086, A328578.

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, Oct 27 2019