A366742 - OEIS

%I #10 Oct 21 2023 01:50:12

%S 1,2,2,3,2,4,2,2,3,4,2,6,2,4,4,5,2,6,2,6,4,4,2,4,3,4,2,6,2,8,2,2,4,4,

%T 4,9,2,4,4,4,2,8,2,6,6,4,2,10,3,6,4,6,2,4,4,4,4,4,2,12,2,4,6,3,4,8,2,

%U 6,4,8,2,6,2,4,6,6,4,8,2,10,5,4,2,12,4,4

%N The number of divisors of the least coreful infinitary divisor of n.

%C The sum of divisors of the least coreful infinitary divisor of n is A366744(n).

%H Amiram Eldar, <a href="/A366742/b366742.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000005(A365296(n)).

%F a(n) = A000005(n) if and only if n is in A138302.

%F Multiplicative with a(p^e) = A006519(e) + 1.

%t f[p_, e_] := 2^IntegerExponent[e, 2] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

%o (PARI) a(n) = vecprod(apply(x -> 2^valuation(x, 2) + 1, factor(n)[, 2]));

%Y Cf. A000005, A006519, A138302, A365296, A366743, A366744.

%K nonn,easy,mult

%O 1,2

%A _Amiram Eldar_, Oct 19 2023