A336320 -id:A336320 - cp's OEIS frontend

A336476 a(n) = gcd(A000593(n), A336475(n)).

1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 12, 1, 2, 1, 2, 2, 4, 2, 2, 2, 1, 2, 4, 2, 2, 12, 2, 1, 12, 2, 4, 1, 2, 2, 4, 2, 2, 4, 2, 2, 6, 2, 2, 2, 3, 1, 12, 2, 2, 4, 4, 2, 4, 2, 2, 12, 2, 2, 2, 1, 4, 12, 2, 2, 12, 4, 2, 1, 2, 2, 2, 2, 4, 4, 2, 2, 1, 2, 2, 4, 4, 2, 12, 2, 2, 6, 28, 2, 4, 2, 20, 2, 2, 3, 6, 1, 2, 12, 2, 2, 24

Offset: 1

Antti Karttunen, Jul 30 2020

nonn

All odd terms k in A001599 (Ore's Harmonic numbers) satisfy a(k) = A336475(k).

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A000265, A000593, A001227, A001599, A324121, A336475.

Cf. also A324058, A336320.

A000593(n) = sigma(n>>valuation(n, 2));
A336475(n) = { my(f=factor(n)); prod(i=1, #f~, if(2==f[i,1],1,(1+f[i,2]) * (f[i,1]^f[i,2]))); };
A336476(n) = gcd(A000593(n), A336475(n));

a(n) = gcd(A000593(n), A336475(n)).

a(n) = A324121(A000265(n)).

A336648 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336476(i) = A336476(j), for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 3, 1, 2, 1, 2, 2, 4, 2, 2, 2, 1, 2, 4, 2, 2, 3, 2, 1, 3, 2, 4, 1, 2, 2, 4, 2, 2, 4, 2, 2, 5, 2, 2, 2, 6, 1, 3, 2, 2, 4, 4, 2, 4, 2, 2, 3, 2, 2, 2, 1, 4, 3, 2, 2, 3, 4, 2, 1, 2, 2, 2, 2, 4, 4, 2, 2, 1, 2, 2, 4, 4, 2, 3, 2, 2, 5, 7, 2, 4, 2, 8, 2, 2, 6, 5, 1, 2, 3, 2, 2, 9

Offset: 1

Antti Karttunen, Jul 31 2020

nonn

Restricted growth sequence transform of A336476.

For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

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

Cf. A000593, A336475, A336476.

Cf. also A003602, A324400, A336320.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A000593(n) = sigma(n>>valuation(n, 2));
A336475(n) = { my(f=factor(n)); prod(i=1, #f~, if(2==f[i,1],1,(1+f[i,2]) * (f[i,1]^f[i,2]))); };
A336476(n) = gcd(A000593(n), A336475(n));
v336648 = rgs_transform(vector(up_to,n,A336476(n)));
A336648(n) = v336648[n];

cp's OEIS Frontend

A336476 a(n) = gcd(A000593(n), A336475(n)).

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