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A329029 a(n) = A069359(A276086(n)), where A276086 is the primorial base exp-function and A069359(n) = n * Sum_{p|n} 1/p.

%I A329029 #24 Feb 12 2025 09:33:16
%S A329029 0,1,1,5,3,15,1,7,8,31,24,93,5,35,40,155,120,465,25,175,200,775,600,
%T A329029 2325,125,875,1000,3875,3000,11625,1,9,10,41,30,123,12,59,71,247,213,
%U A329029 741,60,295,355,1235,1065,3705,300,1475,1775,6175,5325,18525,1500,7375,8875,30875,26625,92625,7,63,70,287,210,861,84,413,497,1729
%N A329029 a(n) = A069359(A276086(n)), where A276086 is the primorial base exp-function and A069359(n) = n * Sum_{p|n} 1/p.
%C A329029 A380535 gives the indices n where a(n) is a multiple of A053669(n). This can be seen from the formula a(n) = A003557(A276086(n)) * A069359(A328571(n)). The left hand side of the product is a multiple of A053669(n) if and only if A276088(n) > 1, while the right hand side is never a multiple of A053669(n), as it is equal to A329031(n) = A003415(A007947(A276086(n))). - _Antti Karttunen_, Feb 11 2025
%H A329029 Antti Karttunen, <a href="/A329029/b329029.txt">Table of n, a(n) for n = 0..2310</a>
%H A329029 Antti Karttunen, <a href="/A329029/a329029.txt">Data supplement: n, a(n) computed for n = 0..32768</a>
%H A329029 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A329029 a(n) = A069359(A276086(n)).
%F A329029 a(n) = A328572(n) * A329031(n) = A003557(A276086(n)) * A069359(A328571(n)). - _Antti Karttunen_, Feb 11 2025
%o A329029 (PARI) A329029(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); if(e, m *= (p^e); s += (1/p)); n = n\p; p = nextprime(1+p)); (s*m); };
%o A329029 (PARI)
%o A329029 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A329029 A069359(n) = (n*sumdiv(n, d, isprime(d)/d));
%o A329029 A329029(n) = A069359(A276086(n));
%Y A329029 Cf. A003415, A003557, A053669, A069359, A276086, A276088, A328571, A328572, A329031, A380535.
%Y A329029 Coincides with A327860 on the positions given by A276156.
%K A329029 nonn
%O A329029 0,4
%A A329029 _Antti Karttunen_, Nov 07 2019