A353572 Shifted variant of A342002: a(n) = A353571(A276086(n)), where A353571(x) = A003415(A003961(x)) / A003557(A003961(x)) and A276086 is the primorial base exp-function.

0, 1, 1, 8, 2, 11, 1, 10, 12, 71, 19, 92, 2, 13, 17, 86, 24, 107, 3, 16, 22, 101, 29, 122, 4, 19, 27, 116, 34, 137, 1, 14, 16, 103, 27, 136, 18, 131, 167, 886, 244, 1117, 29, 164, 222, 1051, 299, 1282, 40, 197, 277, 1216, 354, 1447, 51, 230, 332, 1381, 409, 1612, 2, 17, 21, 118, 32, 151, 25, 152, 202, 991, 279

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..11550

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to primorial base

Formula

a(n) = A353571(A276086(n)).

a(n) = A342002(A276154(n)).

For all n >= 0, a(n) >= A342002(n).

Prog

(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
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A353571(n) = { my(s=A003961(n)); (A003415(s)/A003557(s)); };
A353572(n) = A353571(A276086(n));

Crossrefs

Cf. A003415, A003557, A003961, A276154, A342002, A349905, A353571, A353573 [= gcd(a(n), A342002(n))], A353574.

Sequence in context: A031110 A084491 A248298 * A084495 A084499 A070487

Adjacent sequences: A353569 A353570 A353571 * A353573 A353574 A353575

Keyword

nonn,base

Author

Antti Karttunen, Apr 27 2022

Status

approved