A322312 a(n) = Product_{d|n, d+1 is prime} prime(1+A286561(n,d+1)), where A286561(n,k) gives the k-valuation of n (for k > 1).

2, 6, 2, 20, 2, 18, 2, 28, 2, 12, 2, 120, 2, 6, 2, 88, 2, 60, 2, 60, 2, 12, 2, 168, 2, 6, 2, 40, 2, 72, 2, 104, 2, 6, 2, 800, 2, 6, 2, 168, 2, 54, 2, 40, 2, 12, 2, 528, 2, 12, 2, 40, 2, 84, 2, 56, 2, 12, 2, 1440, 2, 6, 2, 136, 2, 72, 2, 20, 2, 24, 2, 2240, 2, 6, 2, 20, 2, 36, 2, 528, 2, 12, 2, 720, 2, 6, 2, 112, 2

Offset: 1

Author

Antti Karttunen, Dec 03 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A067513, A185633, A286561, A322313 (rgs-transform), A322314.

Cf. also A293514, A322310.

Programs

PARI

A322312(n) = { my(m=1,p); fordiv(n,d,p=1+d; if(isprime(p), for(i=0,oo,if(n%(p^i),m *= prime(i);break)))); (m); };

Formula

a(n) = Product_{d|n} A000040(1+A286561(n,1+d))^A010051(1+d).

a(n) = A181819(A185633(n)).

For all n, A001222(a(n)) = A067513(n).