A332461 a(n) = Product_{d|n, d>1} A000040(A297113(d)), where A000040(n) gives the n-th prime, and A297113(n) = the excess of n plus the index of the largest dividing prime (A046660 + A061395).

1, 2, 3, 6, 5, 18, 7, 30, 15, 50, 11, 270, 13, 98, 75, 210, 17, 450, 19, 1050, 147, 242, 23, 9450, 35, 338, 105, 3234, 29, 11250, 31, 2310, 363, 578, 245, 47250, 37, 722, 507, 57750, 41, 43218, 43, 9438, 2625, 1058, 47, 727650, 77, 2450, 867, 17238, 53, 22050, 605, 210210, 1083, 1682, 59, 8268750, 61, 1922, 8085, 30030

Offset: 1

Author

Antti Karttunen, Feb 22 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000040, A002110, A046660, A046523, A048675, A061395, A097248, A156552, A297113, A324202, A332462.

Programs

PARI

A297113(n) = if(1==n, 0, (primepi(vecmax(factor(n)[, 1])) + (bigomega(n)-omega(n))));
A332461(n) = if(1==n,1, my(m=1); fordiv(n,d,if(d>1, m *= prime(A297113(d)))); (m));

Formula

a(n) = Product_{d|n, d>1} A000040(A297113(d)).

a(p) = p for all primes p.

For all n >= 0, a(2^n) = A002110(n).

For all n >= 1:

A046523(a(n)) = A324202(n).

A048675(a(n)) = A156552(n).

A097248(a(n)) = A332462(n).