A353571 Prime-shifted variant of A342001: a(n) = A349905(n) / A003557(A003961(n)).

0, 1, 1, 2, 1, 8, 1, 3, 2, 10, 1, 13, 1, 14, 12, 4, 1, 11, 1, 17, 16, 16, 1, 18, 2, 20, 3, 25, 1, 71, 1, 5, 18, 22, 18, 16, 1, 26, 22, 24, 1, 103, 1, 29, 19, 32, 1, 23, 2, 13, 24, 37, 1, 14, 20, 36, 28, 34, 1, 106, 1, 40, 27, 6, 24, 119, 1, 41, 34, 131, 1, 21, 1, 44, 17, 49, 24, 151, 1, 31, 4, 46, 1, 158, 26, 50, 36

Offset: 1

Author

Antti Karttunen, Apr 27 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003415, A003557, A003961, A342001, A349905, A353572.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A353571(n) = { my(s=A003961(n)); (A003415(s)/A003557(s)); };

Formula

a(n) = A342001(A003961(n)) = A349905(n) / A003557(A003961(n)).

For all n >= 1, a(n) >= A342001(n).