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A329043 a(n) = Product_{d|A122111(n), d>1} A008578(1+A286561(n,d)), where A286561(n,d) gives the exponent of the highest power of d dividing n. 3
1, 2, 1, 1, 1, 8, 1, 1, 6, 2, 1, 3, 1, 2, 2, 1, 1, 3, 1, 48, 2, 2, 1, 5, 1, 2, 1, 6, 1, 128, 1, 1, 2, 2, 1, 3, 1, 2, 2, 10, 1, 8, 1, 6, 2, 2, 1, 7, 1, 3, 2, 6, 1, 1, 1, 320, 2, 2, 1, 12, 1, 2, 1, 1, 1, 8, 1, 6, 2, 8, 1, 3, 1, 2, 48, 6, 1, 8, 1, 21, 1, 2, 1, 3072, 1, 2, 2, 20, 1, 8, 1, 6, 2, 2, 1, 11, 1, 1, 1, 1, 1, 8, 1, 20, 8 (list; graph; refs; listen; history; text; internal format)
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|A122111(n), d>1} A008578(1+A286561(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)));

A329043(n) = { my(m=1, v); fordiv(A122111(n), d, if((d>1) && ((v = valuation(n, d))>0), m *= prime(v))); (m); };

CROSSREFS

Cf. A001222, A008578, A122111, A286561, A329036, A329042.

Cf. also A327167.

Sequence in context: A172971 A306702 A240581 * A329042 A171660 A157117

Adjacent sequences:  A329040 A329041 A329042 * A329044 A329045 A329046

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 08 2019

STATUS

approved

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Last modified October 29 18:30 EDT 2020. Contains 338067 sequences. (Running on oeis4.)