cp's OEIS Frontend

A346105 a(n) = A276085(A108951(n)).

%I A346105 #6 Jul 08 2021 14:22:35
%S A346105 0,1,3,2,9,4,39,3,6,10,249,5,2559,40,12,4,32589,7,543099,11,42,250,
%T A346105 10242789,6,18,2560,9,41,233335659,13,6703028889,5,252,32590,48,8,
%U A346105 207263519019,543100,2562,12,7628001653829,43,311878265181039,251,15,10242790,13394639596851069,7,78,19,32592,2561,628284422185342479,10,258,42
%N A346105 a(n) = A276085(A108951(n)).
%C A346105 Additive with a(p^e) = e * A143293(A000720(p)-1), where A143293 is the partial sums of primorials, A002110. (Compare to the formula of A276085).
%H A346105 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A346105 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A346105 a(n) = A276085(A108951(n)).
%o A346105 (PARI)
%o A346105 A002110(n) = prod(i=1,n,prime(i));
%o A346105 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^f[i, 2]) };
%o A346105 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%o A346105 A346105(n) = A276085(A108951(n));
%o A346105 (PARI)
%o A346105 A143293(n) = { if(n==0, return(1)); my(P=1, s=1); forprime(p=2, prime(n), s+=P*=p); s; }; \\ This function from A143293
%o A346105 A346105(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A143293(primepi(f[k, 1])-1)); };
%Y A346105 Cf. A002110, A108951, A143293, A276085, A346108, A346109.
%Y A346105 Cf. also A324886.
%K A346105 nonn
%O A346105 1,3
%A A346105 _Antti Karttunen_, Jul 08 2021