A369762 The sum of unitary divisors of the smallest multiple of n whose prime factorization exponents are all powers of 2.

1, 3, 4, 5, 6, 12, 8, 17, 10, 18, 12, 20, 14, 24, 24, 17, 18, 30, 20, 30, 32, 36, 24, 68, 26, 42, 82, 40, 30, 72, 32, 257, 48, 54, 48, 50, 38, 60, 56, 102, 42, 96, 44, 60, 60, 72, 48, 68, 50, 78, 72, 70, 54, 246, 72, 136, 80, 90, 60, 120, 62, 96, 80, 257, 84, 144

Offset

1,2

Links

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

Formula

a(n) = A034448(A356194(n)).

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

a(n) >= A034448(n), with equality if and only if n is in A138302.

Mathematica

f[p_, e_] := p^(2^Ceiling[Log2[e]]) + 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); }

Crossrefs

Cf. A034448, A138302, A353897, A356194, A369760, A369761.

Sequence in context: A186644 A337177 A125139 * A107224 A026493 A177431

Adjacent sequences: A369759 A369760 A369761 * A369763 A369764 A369765

Keyword

nonn,easy,mult

Author

Amiram Eldar, Jan 31 2024

Status

approved