A351961 - OEIS

A351961

Square array A(n,k) = A156552(gcd(A005940(1+n), A005940(1+k))), read by antidiagonals.

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 2, 1, 4, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 5, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1, 6, 1, 0, 1, 2, 1, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 4, 0, 2, 0, 0

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OFFSET

0,13

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.

LINKS

Table of n, a(n) for n=0..104.

Index entries for sequences related to binary expansion of n

FORMULA

For all x, y >= 0, A(x, y) = A(x, A351960(x,y)) = A(A351960(x,y), y).

EXAMPLE

The top left corner of the array:

n= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

-----|--------------------------------------------------------------

k= 0 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

1 | 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,

2 | 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0,

3 | 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1,

4 | 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0,

5 | 0, 1, 2, 1, 0, 5, 2, 1, 0, 1, 2, 5, 0, 5, 2, 1, 0, 1,

6 | 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 2, 0, 6, 6, 0, 0, 0,

7 | 0, 1, 0, 3, 0, 1, 0, 7, 0, 1, 0, 3, 0, 1, 0, 7, 0, 1,

8 | 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8,

9 | 0, 1, 0, 1, 4, 1, 0, 1, 0, 9, 4, 1, 4, 1, 0, 1, 0, 1,

10 | 0, 0, 2, 0, 4, 2, 2, 0, 0, 4, 10, 2, 4, 2, 2, 0, 0, 0,

11 | 0, 1, 2, 3, 0, 5, 2, 3, 0, 1, 2, 11, 0, 5, 2, 3, 0, 1,

12 | 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, 12, 0, 0, 0, 0, 0,

13 | 0, 1, 2, 1, 0, 5, 6, 1, 0, 1, 2, 5, 0, 13, 6, 1, 0, 1,

14 | 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 2, 0, 6, 14, 0, 0, 0,

15 | 0, 1, 0, 3, 0, 1, 0, 7, 0, 1, 0, 3, 0, 1, 0, 15, 0, 1,

16 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0,

17 | 0, 1, 0, 1, 0, 1, 0, 1, 8, 1, 0, 1, 0, 1, 0, 1, 0, 17,

PROG

(PARI)

up_to = 104; \\ 10439 = binomial(144+1, 2)-1

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 };

A351961sq(n, k) = A156552(gcd(A005940(1+n), A005940(1+k)));

A351961list(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] = A351961sq(col, (a-(col))))); (v); };

v351961 = A351961list(up_to);

A351961(n) = v351961[1+n];

CROSSREFS

Cf. A003989, A005940, A156552.

Cf. A001477 (main diagonal).

Cf. also A341520, A351960, A351962.

Sequence in context: A297231 A056620 A316869 * A258772 A178401 A357911

Adjacent sequences: A351958 A351959 A351960 * A351962 A351963 A351964

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Feb 26 2022

STATUS

approved