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The sum of divisors of the largest unitary divisor of n that is a term of A138302.
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%I #8 Nov 10 2023 09:33:53

%S 1,3,4,7,6,12,8,1,13,18,12,28,14,24,24,31,18,39,20,42,32,36,24,4,31,

%T 42,1,56,30,72,32,1,48,54,48,91,38,60,56,6,42,96,44,84,78,72,48,124,

%U 57,93,72,98,54,3,72,8,80,90,60,168,62,96,104,1,84,144,68,126

%N The sum of divisors of the largest unitary divisor of n that is a term of A138302.

%H Amiram Eldar, <a href="/A367171/b367171.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = (p^(A048298(e)+1)-1)/(p-1).

%F a(n) = A000203(A367168(n)).

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

%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2)/zeta(3) = 1.368432... (A306633).

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

%o (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] == 1 << valuation(f[i, 2], 2), (f[i, 1]^(f[i, 2]+1)-1)/(f[i, 1]-1), 1));}

%Y Cf. A000203, A048298, A138302, A306633, A367168, A367169, A367170.

%Y Similar sequences: A351568, A351569.

%K nonn,easy,mult

%O 1,2

%A _Amiram Eldar_, Nov 07 2023