A389094 Square array, A(n, k) = A009194(A389088(n, k)), read by descending antidiagonals.

1, 1, 1, 6, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 4, 1, 1, 7, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 7, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 15, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 28, 3, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..22155; the first 210 antidiagonals of the array

Index entries for sequences computed from indices in prime factorization.

Index entries for sequences related to sigma(n).

Formula

A(n, k) = gcd(A389088(n, k), A389093(n, k)).

A(n, k) = A389088(n, k) / A388996(n, k).

A(n, k) = A389093(n, k) / A388995(n, k).

Example

The top left corner of the array:
k=  | 1  2  3  4  5  6   7  8  9  10  11  12 13  14 15 16 17 18 19  20
----+--------------------------------------------------------------------
1   | 1, 1, 6, 1, 2, 4,  2, 1, 3,  2,  2, 12, 2, 28, 6, 1, 2, 1, 2, 10,
2   | 1, 1, 3, 1, 1, 3,  1, 1, 1,  1,  3, 15, 3, 13, 3, 1, 1, 1, 3,  1,
3   | 1, 1, 1, 1, 1, 1,  1, 1, 1,  1,  5,  1, 1,  1, 7, 1, 5, 1, 1, 13,
4   | 1, 1, 7, 1, 1, 7,  1, 1, 1,  1,  1,  7, 1,  1, 7, 1, 1, 1, 1,  1,
5   | 1, 1, 1, 1, 1, 1,  1, 1, 1,  1,  1,  1, 1,  1, 1, 1, 1, 1, 1, 17,
6   | 1, 1, 1, 1, 1, 1,  1, 1, 1, 19,  1,  1, 1,  1, 1, 1, 1, 1, 1,  1,
7   | 1, 1, 1, 1, 1, 1,  1, 1, 1,  1,  1,  1, 1,  1, 1, 1, 1, 1, 1, 29,
8   | 1, 1, 1, 1, 1, 1, 19, 1, 1,  1,  1,  1, 1, 19, 1, 1, 1, 1, 1,  1,
9   | 1, 1, 1, 1, 1, 1,  1, 1, 1,  1,  1,  1, 1,  1, 1, 1, 1, 1, 1,  1,
10  | 1, 1, 1, 1, 1, 1,  1, 1, 1,  1,  1,  1, 1,  1, 1, 1, 1, 1, 1,  1,
11  | 1, 1, 1, 1, 1, 1,  1, 1, 1,  1,  1,  1, 1,  1, 1, 1, 1, 1, 1,  1,
12  | 1, 1, 1, 1, 1, 1,  1, 1, 1,  1, 31,  1, 1,  1, 1, 1, 1, 1, 1,  1,

Prog

(PARI)
up_to = 22155; \\ = binomial(210+1, 2)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f);
A108546list(up_to) = { my(v=vector(up_to), p, q); v[1] = 2; v[2] = 3; v[3] = 5; for(n=4, up_to, p = v[n-2]; q = nextprime(1+p); while(q%4 != p%4, q=nextprime(1+q)); v[n] = q); (v); };
v108546 = A108546list(up_to);
A108546(n) = v108546[n];
A108548(n) = { my(f=factor(n)); f[, 1] = apply(A108546, apply(primepi, f[, 1])); factorback(f); };
A332806list(up_to) = { my(v=vector(2), xs=Map(), lista=List([]), p, q, u); v[2] = 3; v[1] = 5; mapput(xs, 1, 1); mapput(xs, 2, 2); mapput(xs, 3, 3);  for(n=4, up_to, p = v[2-(n%2)]; q = nextprime(1+p); while(q%4 != p%4, q=nextprime(1+q)); v[2-(n%2)] = q; mapput(xs, primepi(q), n)); for(i=1, oo, if(!mapisdefined(xs, i, &u), return(Vec(lista)), listput(lista, prime(u)))); };
v332806 = A332806list(up_to);
A332806(n) = v332806[n];
A332808(n) = { my(f=factor(n)); f[, 1] = apply(A332806, apply(primepi, f[, 1])); factorback(f); };
A332818(n) = A108548(A003961(A332808(n)));
A389088sq(row, col) = { my(x=2*col); for(i=2, row, x = A332818(x)); (x); };
A389094sq(row, col)  = ((x->gcd(x, sigma(x)))(A389088sq(row, col)));
A389094list(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] = A389094sq(col, (a-(col-1))))); (v); };
v389094 = A389094list(up_to);
A389094(n) = v389094[n];

Crossrefs

Cf. A009194, A332818, A389088, A389093, A388995, A388996.

Cf. also A355925.

Sequence in context: A324394 A064793 A355925 * A275109 A331735 A345948

Adjacent sequences: A389091 A389092 A389093 * A389095 A389096 A389097

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 24 2025

Status

approved