A350063 a(n) is the smallest number with the same prime signature as A322993(n), with a(1) = 0.

0, 1, 1, 2, 1, 2, 1, 2, 2, 4, 1, 2, 1, 2, 2, 6, 1, 2, 1, 2, 4, 6, 1, 2, 2, 6, 2, 6, 1, 6, 1, 2, 2, 6, 2, 8, 1, 2, 6, 6, 1, 2, 1, 2, 2, 24, 1, 2, 2, 4, 6, 2, 1, 2, 4, 2, 6, 12, 1, 2, 1, 6, 2, 12, 2, 6, 1, 6, 2, 2, 1, 6, 1, 6, 2, 6, 2, 6, 1, 2, 6, 6, 1, 12, 6, 30, 24, 24, 1, 12, 4, 6, 12, 60, 6, 6, 1, 4, 6, 6, 1

Offset: 1

Author

Antti Karttunen, Jan 29 2022

Keywords

• nonn

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000265, A046523, A156552, A322993, A350062, A350064, A350065 (rgs-transform).

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
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 };
A350063(n) = if(1==n,0,A046523(A000265(A156552(n))));

Formula

a(1) = 0; for n > 1, a(n) = A046523(A322993(n)) = A046523(A000265(A156552(n))).