A329043 a(n) = Product_{d|A122111(n), d>1} A008578(1+A286561(n,d)), where A286561(n,d) gives the exponent of the highest power of d dividing n.

1, 2, 1, 1, 1, 8, 1, 1, 6, 2, 1, 3, 1, 2, 2, 1, 1, 3, 1, 48, 2, 2, 1, 5, 1, 2, 1, 6, 1, 128, 1, 1, 2, 2, 1, 3, 1, 2, 2, 10, 1, 8, 1, 6, 2, 2, 1, 7, 1, 3, 2, 6, 1, 1, 1, 320, 2, 2, 1, 12, 1, 2, 1, 1, 1, 8, 1, 6, 2, 8, 1, 3, 1, 2, 48, 6, 1, 8, 1, 21, 1, 2, 1, 3072, 1, 2, 2, 20, 1, 8, 1, 6, 2, 2, 1, 11, 1, 1, 1, 1, 1, 8, 1, 20, 8

Offset: 1

Author

Antti Karttunen, Nov 08 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A001222, A008578, A122111, A286561, A329036, A329042.

Cf. also A327167.

Programs

PARI

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A329043(n) = { my(m=1,v); fordiv(A122111(n),d,if((d>1) && ((v = valuation(n,d))>0), m *= prime(v))); (m); };

Formula

a(n) = Product_{d|A122111(n), d>1} A008578(1+A286561(n,d)).

1+A001222(a(n)) = A329036(n).