A339877 a(n) = A336467(A122111(n)).

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 9, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 9, 1, 1, 3, 1, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 9, 7, 1, 3, 1, 3, 1, 3, 1, 3, 1, 1, 9, 3, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 7, 1, 3, 9, 1, 1, 3, 1, 1, 9

Offset

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..12166

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

Index entries for sequences computed from indices in prime factorization

Formula

For noncomposite n, a(n) = 1, for composite n, a(n) = A000265(A105560(n)+1) * a(A064989(n)).

a(n) = A336467(A122111(n)).

Prog

(PARI)
A000265(n) = (n>>valuation(n, 2));
A122111(n) = if(1==n, n, my(f=factor(n), es=Vecrev(f[, 2]), is=concat(apply(primepi, Vecrev(f[, 1])), [0]), pri=0, m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A336467(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265(f[k, 1]+1))^f[k, 2])); };
A339877(n) = A336467(A122111(n));
(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)};
A105560(n) = if(1==n, n, prime(bigomega(n)));
A339877(n) = if(1==n||isprime(n), 1, A000265(A105560(n)+1) * A339877(A064989(n)));

Crossrefs

Cf. A000265, A064989, A105560, A122111, A336467.

Cf. also A339876, A334108.

Sequence in context: A214709 A369317 A060268 * A030328 A176563 A093148

Adjacent sequences: A339874 A339875 A339876 * A339878 A339879 A339880

Keyword

nonn

Author

Antti Karttunen, Dec 25 2020

Status

approved