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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. 3
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 (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|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

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Last modified September 21 02:11 EDT 2020. Contains 337266 sequences. (Running on oeis4.)