A331309 a(n) = A000005(A225546(n)), where A000005 gives the number of divisors of n.

1, 2, 3, 2, 5, 4, 9, 4, 3, 6, 17, 6, 33, 10, 7, 2, 65, 6, 129, 10, 11, 18, 257, 8, 5, 34, 9, 18, 513, 8, 1025, 4, 19, 66, 13, 4, 2049, 130, 35, 12, 4097, 12, 8193, 34, 15, 258, 16385, 6, 9, 10, 67, 66, 32769, 12, 21, 20, 131, 514, 65537, 14, 131073, 1026, 27, 4, 37, 20, 262145, 130, 259, 14, 524289, 8, 1048577, 2050, 15

Offset

1,2

Links

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

Formula

a(n) = A000005(A225546(n)).

Prog

(PARI)
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A331309(n) = if(1==n, 1, my(f=factor(n), u=#binary(vecmax(f[, 2])), prods=vector(u, x, 1), m=1, e); for(i=1, u, for(k=1, #f~, if(bitand(f[k, 2], m), prods[i] *= f[k, 1])); m<<=1); prod(i=1, u, 1+A048675(prods[i])));

Crossrefs

Cf. A000005, A048675, A225546, A331287, A331308, A331591.

Sequence in context: A075365 A268466 A075274 * A178144 A357987 A135737

Adjacent sequences: A331306 A331307 A331308 * A331310 A331311 A331312

Keyword

nonn

Author

Antti Karttunen, Jan 21 2020

Status

approved