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%I #8 Feb 03 2024 10:16:35
%S 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,
%T 42,82,40,30,72,32,257,48,54,48,50,38,60,56,102,42,96,44,60,60,72,48,
%U 68,50,78,72,70,54,246,72,136,80,90,60,120,62,96,80,257,84,144
%N The sum of unitary divisors of the smallest multiple of n whose prime factorization exponents are all powers of 2.
%H Amiram Eldar, <a href="/A369762/b369762.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A034448(A356194(n)).
%F Multiplicative with a(p^e) = p^(2^ceiling(log_2(e))) + 1.
%F a(n) >= A034448(n), with equality if and only if n is in A138302.
%t f[p_, e_] := p^(2^Ceiling[Log2[e]]) + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o (PARI) s(n) = {my(e=logint(n, 2)); if(n == 2^e, n, 2^(e+1))};
%o a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^s(f[i,2]) + 1);}
%Y Cf. A034448, A138302, A353897, A356194, A369760, A369761.
%K nonn,easy,mult
%O 1,2
%A _Amiram Eldar_, Jan 31 2024