A365425 The least number with the prime signature of the odd part of A163511(n): a(n) = A046523(A000265(A163511(n))).

1, 1, 1, 2, 1, 4, 2, 2, 1, 8, 4, 4, 2, 6, 2, 2, 1, 16, 8, 8, 4, 12, 4, 4, 2, 12, 6, 6, 2, 6, 2, 2, 1, 32, 16, 16, 8, 24, 8, 8, 4, 36, 12, 12, 4, 12, 4, 4, 2, 24, 12, 12, 6, 30, 6, 6, 2, 12, 6, 6, 2, 6, 2, 2, 1, 64, 32, 32, 16, 48, 16, 16, 8, 72, 24, 24, 8, 24, 8, 8, 4, 72, 36, 36, 12, 60, 12, 12, 4, 36, 12, 12, 4, 12, 4, 4, 2

Offset: 0

Author

Antti Karttunen, Sep 03 2023

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16385

Crossrefs

Cf. A000265, A046523, A064989, A163511, A336158.

Cf. also A278531.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A365425(n) = A046523(A000265(A163511(n)));

Formula

a(n) = A336158(A163511(n)) = A046523(A064989(A163511(n))).

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).