login
A369762
The sum of unitary divisors of the smallest multiple of n whose prime factorization exponents are all powers of 2.
3
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
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
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Jan 31 2024
STATUS
approved