A331287 a(n) = gcd(n, A225546(n)).

1, 2, 1, 1, 1, 2, 1, 2, 9, 2, 1, 12, 1, 2, 1, 1, 1, 18, 1, 4, 1, 2, 1, 24, 1, 2, 9, 4, 1, 2, 1, 2, 1, 2, 1, 9, 1, 2, 1, 8, 1, 2, 1, 4, 9, 2, 1, 4, 1, 2, 1, 4, 1, 18, 1, 8, 1, 2, 1, 12, 1, 2, 9, 1, 1, 2, 1, 4, 1, 2, 1, 18, 1, 2, 3, 4, 1, 2, 1, 80, 1, 2, 1, 12, 1, 2, 1, 8, 1, 18, 1, 4, 1, 2, 1, 8, 1, 2, 9, 1, 1, 2, 1, 8, 1

Offset: 1

Author

Antti Karttunen, Jan 20 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11250
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A225546, A225547 (fixed points), A297845, A331288, A331310, A331311.

Programs

PARI

A331287(n) = gcd(n, A225546(n));

PARI

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A331287(n) = if(1==n,1,my(f=factor(n),u=#binary(vecmax(f[, 2])),prods=vector(u,x,1),m=1,e); for(i=1,u,if(!(n%prime(i)),for(k=1,#f~, if(bitand(f[k,2],m),prods[i] *= f[k,1]))); m<<=1); prod(i=1,u,prime(i)^min(valuation(n,prime(i)),A048675(prods[i]))));

Formula

a(n) = gcd(n, A225546(n)).

a(n) = A331310(n) * A331311(n).

a(A297845(n,9)) = A297845(a(n),9). - Peter Munn, Jan 24 2020