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A369761
The sum of divisors of the smallest multiple of n whose prime factorization exponents are all powers of 2.
3
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
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
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Jan 31 2024
STATUS
approved