A356156 The nearest common ancestor of n and gcd(n, sigma(n)) in the Doudna tree (A005940).

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 1, 2, 1, 12, 1, 2, 1, 28, 1, 6, 1, 1, 3, 2, 1, 1, 1, 2, 1, 10, 1, 3, 1, 2, 3, 2, 1, 2, 1, 1, 3, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 1, 1, 1, 3, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 5, 1, 2, 3, 2, 1, 2, 5, 2, 1, 2, 5, 12, 1, 1, 3, 1, 1, 3, 1, 2, 3

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A348041(n, A009194(n)) = A348041(n, gcd(n, A000203(n))).

Prog

(PARI)
Abincompreflen(n, m) = { my(x=binary(n), y=binary(m), u=min(#x, #y)); for(i=1, u, if(x[i]!=y[i], return(i-1))); (u); };
Abinprefix(n, k) = { my(digs=binary(n)); fromdigits(vector(k, i, digs[i]), 2); };
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}; \\ From A156552
A348040sq(x, y) = Abincompreflen(A156552(x), A156552(y));
A348041sq(x, y) = A005940(1+Abinprefix(A156552(x), A348040sq(x, y)));
A356156(n) = A348041sq(n, gcd(n, sigma(n)));

Crossrefs

Cf. A000203, A007691 (fixed points), A009194, A348040, A348041.

Cf. also A347879, A356157, A356158, A356306.

Sequence in context: A260340 A040037 A344877 * A356157 A389446 A333461

Adjacent sequences: A356153 A356154 A356155 * A356157 A356158 A356159

Keyword

nonn

Author

Antti Karttunen, Jul 30 2022

Status

approved