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A367171 The sum of divisors of the largest unitary divisor of n that is a term of A138302.

%I A367171 #8 Nov 10 2023 09:33:53
%S A367171 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 A367171 42,1,56,30,72,32,1,48,54,48,91,38,60,56,6,42,96,44,84,78,72,48,124,
%U A367171 57,93,72,98,54,3,72,8,80,90,60,168,62,96,104,1,84,144,68,126
%N A367171 The sum of divisors of the largest unitary divisor of n that is a term of A138302.
%H A367171 Amiram Eldar, <a href="/A367171/b367171.txt">Table of n, a(n) for n = 1..10000</a>
%F A367171 Multiplicative with a(p^e) = (p^(A048298(e)+1)-1)/(p-1).
%F A367171 a(n) = A000203(A367168(n)).
%F A367171 a(n) <= A000203(n), with equality if and only if n is in A138302.
%F A367171 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2)/zeta(3) = 1.368432... (A306633).
%t A367171 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 A367171 (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 A367171 Cf. A000203, A048298, A138302, A306633, A367168, A367169, A367170.
%Y A367171 Similar sequences: A351568, A351569.
%K A367171 nonn,easy,mult
%O A367171 1,2
%A A367171 _Amiram Eldar_, Nov 07 2023