A356158 a(n) = gcd(n, A347879(n)).

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

Offset

1,2

Comments

The fixed points of this sequence is given by the union of {2} and A336702.

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) = gcd(n, A347879(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)));
A347879(n) = A348041sq(n, sigma(n));
A356158(n) = gcd(n, A347879(n));

Crossrefs

Cf. A000203, A336702, A347879, A348040, A348041.

Cf. also A356156, A356157, A356308.

Sequence in context: A086545 A337395 A126083 * A071416 A053589 A055770

Adjacent sequences: A356155 A356156 A356157 * A356159 A356160 A356161

Keyword

nonn

Author

Antti Karttunen, Jul 30 2022

Status

approved