A368991 - OEIS

%I #9 Jan 11 2024 20:04:43

%S 0,0,0,0,0,1,1,1,1,1,1,2,2,3,3,3,3,3,3,4,4,5,5,6,6,6,6,7,7,8,8,8,8,8,

%T 8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,15,15,16,16,17,17,18,18,18,

%U 18,19,19,20,20,20,20,20,20,20,20,21,21,22,22,22,22,23,23,24,24,25,25,25,25,26,26,27,27,28

%N Doudna-gram for nondeficient numbers; Partial sums of A368990.

%H Antti Karttunen, <a href="/A368991/b368991.txt">Table of n, a(n) for n = 0..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(0) = 0, and for n > 0, a(n) = a(n-1) + A368990(n).

%o (PARI)

%o up_to = 65537;

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o A294936(n) = (sigma(n)>=(2*n));

%o A368990(n) = A294936(A005940(1+n));

%o A368991list(up_to) = { my(v=vector(up_to), s=A368990(0)); for(i=1, up_to, s += A368990(i); v[i] = s); (v); };

%o v368991 = A368991list(up_to);

%o A368991(n) = if(!n, A368990(0), v368991[n]);

%Y Partial sums of A368990.

%Y Cf. A005940, A023196, A294936, A324055.

%Y Cf. also A368910, A368993.

%K nonn

%O 0,12

%A _Antti Karttunen_, Jan 11 2024