A307408 a(n) = (A001222(n) - 1)*A001221(n) + 2.

2, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 8, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 11, 2, 4, 6, 7, 4, 8, 2, 6, 4, 8, 2, 10, 2, 4, 6, 6, 4, 8, 2, 10, 5, 4, 2, 11, 4, 4, 4, 8, 2, 11, 4, 6, 4, 4, 4, 12, 2, 6, 6, 8, 2, 8, 2, 8

Offset: 1

Author

Mats Granvik, Apr 07 2019

Keywords

• nonn

Comments

a(n) appears to differ from A000005 at n = 1 and when n is a term of A320632. Verified up to n=3000.

See also Charlie Neder's May 14 2019 comment in A307409.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..13440
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Two more than A307409.

Cf. A001221, A001222, A000005, A320632.

Programs

Mathematica

a[n_] := (PrimeOmega[n] - 1)*PrimeNu[n] + 2;
Table[a[n], {n, 1, 104}]

PARI

A307408(n) = 2+((bigomega(n)-1)*omega(n)); \\ Antti Karttunen, Nov 17 2019

Formula

a(n) = (A001222(n) - 1)*A001221(n) + 2.

a(n) = binomial(A001222(n) - 1, 1)*binomial(A001221(n), 1) + 2.

a(n) = A307409(n) + 2.