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

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

1,3

Links

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

Formula

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).

Prog

(PARI)
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)));

Crossrefs

Cf. A001615, A003557, A003961, A064989, A151800, A347385, A351450.

Coincides with A326042 on squarefree numbers (A005117, and apparently on no other numbers).

Cf. also A351441.

Sequence in context: A253193 A027869 A156748 * A075445 A216612 A194447

Adjacent sequences: A351452 A351453 A351454 * A351456 A351457 A351458

Keyword

nonn,mult

Author

Antti Karttunen, Feb 12 2022

Status

approved