A369761 The sum of divisors of the smallest multiple of n whose prime factorization exponents are all powers of 2.

1, 3, 4, 7, 6, 12, 8, 31, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 124, 31, 42, 121, 56, 30, 72, 32, 511, 48, 54, 48, 91, 38, 60, 56, 186, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 363, 72, 248, 80, 90, 60, 168, 62, 96, 104, 511, 84

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000203(A356194(n)).

Multiplicative with a(p^e) = (p^(2^ceiling(log_2(e))+1)-1)/(p-1).

a(n) >= A000203(n), with equality if and only if n is in A138302.

Mathematica

f[p_, e_] := (p^(2^Ceiling[Log2[e]]+1)-1)/(p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) s(n) = {my(e=logint(n, 2)); if(n == 2^e, n, 2^(e+1))};
a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(s(f[i, 2])+1)-1)/(f[i, 1]-1)); }

Crossrefs

Cf. A000203, A138302, A353897, A356194, A369760, A369762.

Sequence in context: A086293 A337708 A348944 * A003981 A360674 A324108

Adjacent sequences: A369758 A369759 A369760 * A369762 A369763 A369764

Keyword

nonn,easy,mult

Author

Amiram Eldar, Jan 31 2024

Status

approved