A351441 -id:A351441 - cp's OEIS frontend

A351450 a(n) = A064989(A048250(A003961(n))).

1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 5, 2, 4, 2, 2, 1, 3, 2, 2, 1, 4, 5, 6, 2, 1, 4, 2, 2, 1, 2, 17, 1, 10, 3, 2, 2, 10, 2, 8, 1, 7, 4, 2, 5, 2, 6, 8, 2, 2, 1, 6, 4, 6, 2, 5, 2, 4, 1, 29, 2, 13, 17, 4, 1, 4, 10, 4, 3, 12, 2, 31, 2, 3, 10, 2, 2, 10, 8, 10, 1, 2, 7, 12, 4, 3, 2, 2, 5, 25, 2, 8, 6, 34, 8, 2

Offset: 1

Antti Karttunen, Feb 11 2022

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

Cf. A003961, A048250, A064989, A151800, A351449, A351451 [= a(A055231(n))].

Cf. also A351441.

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
A064989(n) = { my(f = factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A351450(n) = A064989(A048250(A003961(n)));

Multiplicative with a(p^e) = A064989(q+1), where q = nextPrime(p) = A151800(p).

a(n) = A064989(A048250(A003961(n))).

A351455 a(n) = A064989(A001615(A003961(n))).

Original entry on oeis.org

1, 1, 2, 2, 1, 2, 2, 4, 6, 1, 5, 4, 4, 2, 2, 8, 3, 6, 2, 2, 4, 5, 6, 8, 5, 4, 18, 4, 1, 2, 17, 16, 10, 3, 2, 12, 10, 2, 8, 4, 7, 4, 2, 10, 6, 6, 8, 16, 14, 5, 6, 8, 6, 18, 5, 8, 4, 1, 29, 4, 13, 17, 12, 32, 4, 10, 4, 6, 12, 2, 31, 24, 3, 10, 10, 4, 10, 8, 10, 8, 54, 7, 12, 8, 3, 2, 2, 20, 25, 6, 8

Offset: 1

Antti Karttunen, Feb 12 2022

Antti Karttunen, Table of n, a(n) for n = 1..20000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A001615, A003557, A003961, A064989, A151800, A347385, A351450.
Coincides with A326042 on squarefree numbers (A005117, and apparently on no other numbers).
Cf. also A351441.

A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A064989(n) = { my(f = factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A351455(n) = A064989(A001615(A003961(n)));

Multiplicative with a(p^e) = A064989((q+1)*q^(e-1)), where q = nextPrime(p) = A151800(p).
a(n) = A064989(A001615(A003961(n))) = A064989(A347385(A003961(n))).
a(n) = A003557(n) * A351450(n).

cp's OEIS Frontend

A351450 a(n) = A064989(A048250(A003961(n))).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula