A328831 - OEIS

%I #8 Nov 01 2019 18:39:08

%S 0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,2,0,0,0,1,0,0,1,0,0,1,0,0,0,1,

%T 0,1,0,0,0,1,0,0,0,0,0,1,1,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,1,

%U 0,0,0,1,0,0,0,0,0,1,0,2,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0

%N Number of distinct prime factors p such that p^p is a divisor of n-th number > 0 that is a sum of distinct primorial numbers, A276156(n).

%H Antti Karttunen, <a href="/A328831/b328831.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

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

%F a(n) = A129251(A276156(n)).

%o (PARI)

%o A129251(n) = { my(f = factor(n)); sum(k=1, #f~, (f[k, 2]>=f[k, 1])); };

%o A276156(n) = { my(p=2,pr=1,s=0); while(n,if(n%2,s += pr); n >>= 1; pr *= p; p = nextprime(1+p)); (s); };

%o A328831(n) = A129251(A276156(n));

%Y Cf. A129251, A276156.

%Y Cf. A328832 (gives A276156(k) for those k for which a(k) = 0).

%K nonn

%O 1,20

%A _Antti Karttunen_, Oct 30 2019