A389095 Square array, A(n, k) = A007814(A389093(n, k)), read by descending antidiagonals.

0, 0, 2, 2, 0, 1, 0, 3, 0, 3, 1, 3, 4, 0, 1, 2, 5, 2, 4, 0, 2, 3, 1, 2, 4, 3, 0, 1, 0, 3, 3, 5, 2, 3, 0, 2, 0, 0, 3, 1, 2, 3, 3, 0, 1, 1, 2, 0, 4, 2, 4, 2, 3, 0, 3, 2, 3, 1, 0, 3, 1, 2, 3, 4, 0, 1, 2, 3, 1, 3, 0, 3, 2, 5, 2, 4, 0, 5, 1, 4, 3, 2, 1, 0, 4, 1, 2, 4, 6, 0, 1, 3, 4, 5, 4, 1, 2, 0, 3, 3, 8, 2, 6, 0, 2

Offset

1,3

Comments

The 2-adic valuations of entries in array A389093.

Links

Antti Karttunen, Table of n, a(n) for n = 1..22155

Index entries for sequences computed from indices in prime factorization.

Index entries for sequences related to sigma(n).

Formula

A(n, k) = A336937(A389088(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 21 22 23 24
----+------------------------------------------------------------------------
1   | 0, 0, 2, 0, 1, 2, 3, 0, 0, 1, 2, 2, 1, 3, 3, 0, 1, 0, 2, 1, 5, 2, 3, 2,
2   | 2, 0, 3, 3, 5, 1, 3, 0, 2, 3, 3, 4, 4, 1, 6, 2, 4, 0, 3, 6, 4, 1, 3, 1,
3   | 1, 0, 4, 2, 2, 3, 3, 0, 1, 1, 3, 5, 2, 2, 5, 1, 2, 0, 4, 3, 6, 2, 6, 3,
4   | 3, 0, 4, 4, 5, 1, 4, 0, 3, 2, 4, 5, 5, 1, 6, 3, 6, 0, 4, 6, 5, 1, 4, 1,
5   | 1, 0, 3, 2, 2, 2, 3, 0, 1, 1, 4, 4, 2, 2, 4, 1, 2, 0, 6, 3, 5, 3, 3, 2,
6   | 2, 0, 3, 3, 4, 1, 3, 0, 2, 2, 3, 4, 5, 1, 5, 2, 7, 0, 3, 5, 4, 1, 3, 1,
7   | 1, 0, 3, 2, 2, 2, 4, 0, 1, 1, 6, 4, 2, 3, 4, 1, 2, 0, 3, 3, 6, 5, 5, 2,
8   | 2, 0, 3, 3, 5, 1, 3, 0, 2, 3, 3, 4, 7, 1, 6, 2, 4, 0, 3, 6, 4, 1, 3, 1,
9   | 1, 0, 4, 2, 2, 3, 6, 0, 1, 1, 3, 5, 2, 5, 5, 1, 2, 0, 5, 3, 9, 2, 3, 3,
10  | 3, 0, 4, 4, 8, 1, 4, 0, 3, 5, 4, 5, 5, 1, 9, 3, 7, 0, 4, 9, 5, 1, 4, 1,
11  | 1, 0, 6, 2, 2, 5, 3, 0, 1, 1, 5, 7, 2, 2, 7, 1, 2, 0, 3, 3, 8, 4, 3, 5,
12  | 5, 0, 6, 6, 7, 1, 6, 0, 5, 2, 6, 7, 9, 1, 8, 5, 7, 0, 6, 8, 7, 1, 6, 1,
13  | 1, 0, 3, 2, 2, 2, 5, 0, 1, 1, 3, 4, 2, 4, 4, 1, 2, 0, 3, 3, 7, 2, 4, 2,
14  | 2, 0, 3, 3, 6, 1, 3, 0, 2, 4, 3, 4, 4, 1, 7, 2, 4, 0, 3, 7, 4, 1, 3, 1,
15  | 1, 0, 5, 2, 2, 4, 3, 0, 1, 1, 3, 6, 2, 2, 6, 1, 2, 0, 4, 3, 7, 2, 5, 4,

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); };
A389093sq(row, col) = sigma(A389088sq(row, col));
A389095sq(row, col) = valuation(A389093sq(row, col), 2);
A389095list(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] = A389095sq(col, (a-(col-1))))); (v); };
v389095 = A389095list(up_to);
A389095(n) = v389095[n];

Crossrefs

Cf. A000203, A007814, A332818, A389088, A389093.

Cf. A336937 (the topmost row).

Sequence in context: A263571 A364060 A361292 * A251690 A187752 A295181

Adjacent sequences: A389092 A389093 A389094 * A389096 A389097 A389098

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 24 2025

Status

approved