A346105 - OEIS

%I #6 Jul 08 2021 14:22:35

%S 0,1,3,2,9,4,39,3,6,10,249,5,2559,40,12,4,32589,7,543099,11,42,250,

%T 10242789,6,18,2560,9,41,233335659,13,6703028889,5,252,32590,48,8,

%U 207263519019,543100,2562,12,7628001653829,43,311878265181039,251,15,10242790,13394639596851069,7,78,19,32592,2561,628284422185342479,10,258,42

%N a(n) = A276085(A108951(n)).

%C 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 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F a(n) = A276085(A108951(n)).

%o (PARI)

%o A002110(n) = prod(i=1,n,prime(i));

%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^f[i, 2]) };

%o A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };

%o A346105(n) = A276085(A108951(n));

%o (PARI)

%o 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(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A143293(primepi(f[k, 1])-1)); };

%Y Cf. A002110, A108951, A143293, A276085, A346108, A346109.

%Y Cf. also A324886.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jul 08 2021