A329042 a(n) = Product_{d|n, d>1} A008578(1+A286561(A122111(n),d)), where A286561(x,d) gives the exponent of the highest power of d dividing x.

1, 2, 1, 1, 1, 8, 1, 1, 6, 3, 1, 2, 1, 5, 3, 1, 1, 2, 1, 48, 3, 7, 1, 2, 1, 11, 1, 10, 1, 128, 1, 1, 3, 13, 1, 2, 1, 17, 3, 6, 1, 12, 1, 21, 3, 19, 1, 2, 1, 2, 3, 33, 1, 1, 1, 320, 3, 23, 1, 8, 1, 29, 1, 1, 1, 20, 1, 65, 3, 8, 1, 2, 1, 31, 48, 85, 1, 28, 1, 6, 1, 37, 1, 3072, 1, 41, 3, 42, 1, 8, 1, 133, 3, 43, 1, 2, 1, 1, 1, 1, 1, 44, 1, 66, 12

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = Product_{d|n, d>1} A008578(1+A286561(A122111(n),d)).

1+A001222(a(n)) = A329036(n).

Prog

(PARI)
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A122111(n) = if(1==n, n, prime(bigomega(n))*A122111(A064989(n)));
A329042(n) = { my(m=1, x=A122111(n), v); fordiv(n, d, if((d>1) && ((v = valuation(x, d))>0), m *= prime(v))); (m); };

Crossrefs

Cf. A001222, A008578, A122111, A286561, A329036, A329043.

Cf. also A329037.

Sequence in context: A306702 A240581 A329043 * A171660 A157117 A322143

Adjacent sequences: A329039 A329040 A329041 * A329043 A329044 A329045

Keyword

nonn

Author

Antti Karttunen, Nov 08 2019

Status

approved