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A351960
Square array A(n,k) = A156552(A005940(1+n) + A005940(1+k)), read by antidiagonals.
5
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 9, 7, 7, 7, 7, 7, 9, 6, 16, 6, 6, 6, 6, 16, 6, 7, 9, 11, 9, 9, 9, 11, 9, 7, 16, 6, 16, 32, 16, 16, 32, 16, 6, 16, 15, 11, 9, 11, 17, 11, 17, 11, 9, 11, 15, 32, 64, 32, 16, 32, 10, 10, 32, 16, 32, 64, 32, 65, 17, 13, 17, 11, 17, 13, 17, 11, 17, 13, 17, 65
OFFSET
0,2
COMMENTS
The indices run as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), etc. The array is symmetric.
EXAMPLE
The top left corner of the array:
|n= 0 1 2 3 4 5 6 7 8 9 10 11 12
-----+--------------------------------------------------------------------------
k= 0 | 1, 2, 3, 4, 5, 8, 9, 6, 7, 16, 15, 32, 65,
1 | 2, 3, 4, 5, 8, 7, 16, 9, 6, 11, 64, 17, 14,
2 | 3, 4, 5, 8, 7, 6, 11, 16, 9, 32, 13, 10, 35,
3 | 4, 5, 8, 7, 6, 9, 32, 11, 16, 17, 128, 15, 512,
4 | 5, 8, 7, 6, 9, 16, 17, 32, 11, 10, 19, 64, 21,
5 | 8, 7, 6, 9, 16, 11, 10, 17, 32, 15, 18, 13, 1024,
6 | 9, 16, 11, 32, 17, 10, 13, 64, 15, 128, 23, 18, 129,
7 | 6, 9, 16, 11, 32, 17, 64, 15, 10, 13, 256, 19, 34,
8 | 7, 6, 9, 16, 11, 32, 15, 10, 17, 64, 33, 128, 31,
9 | 16, 11, 32, 17, 10, 15, 128, 13, 64, 19, 12, 33, 20,
10 | 15, 64, 13, 128, 19, 18, 23, 256, 33, 12, 21, 14, 39,
11 | 32, 17, 10, 15, 64, 13, 18, 19, 128, 33, 14, 23, 2048,
12 | 65, 14, 35, 512, 21, 1024, 129, 34, 31, 20, 39, 2048, 25,
13 | 128, 19, 18, 33, 256, 23, 14, 65, 12, 35, 34, 21, 8192,
14 | 35, 512, 21, 1024, 31, 34, 27, 20, 129, 2048, 37, 66, 131,
15 | 64, 13, 128, 19, 18, 33, 12, 23, 256, 65, 1024, 35, 4096,
16 | 11, 32, 17, 10, 15, 64, 19, 128, 13, 18, 65, 256, 27,
PROG
(PARI)
up_to = 104;
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = { my(f = factor(n), p, 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 };
A351960sq(n, k) = A156552(A005940(1+n)+A005940(1+k));
A351960list(up_to) = { my(v = vector(1+up_to), i=0); for(a=0, oo, for(col=0, a, i++; if(i > #v, return(v)); v[i] = A351960sq(col, (a-(col))))); (v); };
v351960 = A351960list(up_to);
A351960(n) = v351960[1+n];
CROSSREFS
Cf. A005408 (main diagonal), A297163 (row/column 0).
Sequence in context: A196238 A087843 A087831 * A372759 A194327 A058032
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Feb 26 2022
STATUS
approved