A329622 a(n) = A056239(n) - A324888(n) = A001222(A108951(n)) - A001222(A324886(n)).

-1, 0, 1, 0, 2, 1, 3, 1, 2, 2, 4, 0, 5, 3, -1, 0, 6, 1, 7, 1, 0, 4, 8, 1, 0, 5, 4, 2, 9, 0, 10, 3, 1, 6, -3, -2, 11, 7, 2, 4, 12, 5, 13, 3, 1, 8, 14, 2, 0, -5, 3, 4, 15, 3, 2, -1, 4, 9, 16, 1, 17, 10, 2, 2, -5, -4, 18, 5, 5, -2, 19, 1, 20, 11, -2, 6, -9, -3, 21, 3, 0, 12, 22, 4, -2, 13, 6, 0, 23, -4, -8, 7, 7, 14, 3

Offset: 1

Author

Antti Karttunen, Nov 18 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A001222, A034386, A056239, A108951, A276086, A324886, A324888, A329619, A329621.

Programs

Mathematica

With[{b = MixedRadix[Reverse@ Prime@ Range@ 500]}, Array[Subtract @@ PrimeOmega@ {#, Function[k, Times @@ Power @@@ # &@ Transpose@ {Prime@ Range@ Length@ k, Reverse@ k}]@ IntegerDigits[#, b]} &@ Apply[Times, Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Times @@ Prime@ Range@ PrimePi@ p, e}]] &, 95]] (* Michael De Vlieger, Nov 18 2019 *)

PARI

A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A329622(n) = { my(u=A108951(n)); (bigomega(u) - bigomega(A276086(u))); };

Formula

a(n) = A056239(n) - A324888(n) = A001222(A108951(n)) - A001222(A324886(n)).