A341624 - OEIS

%I #6 Feb 24 2021 08:19:12

%S 0,0,0,0,0,1,0,0,0,0,0,2,0,0,0,0,0,2,0,1,0,0,0,3,0,0,0,1,0,2,0,0,0,0,

%T 0,4,0,0,0,2,0,2,0,0,0,0,0,4,0,0,0,0,0,3,0,2,0,0,0,5,0,0,0,0,0,2,0,0,

%U 0,1,0,6,0,0,0,0,0,2,0,3,0,0,0,5,0,0,0,1,0,4,0,0,0,0,0,5,0,0,0,2,0,2,0,1,0,0,0,6,0,0,0,3,0,2,0,0,0,0,0,1

%N a(n) = 0 if n is a deficient number, otherwise a(n) is the number of nondeficient divisors of the last number in the iteration x -> A003961(x) (starting from x=n) for which that count (A341620) is nonzero.

%H Antti Karttunen, <a href="/A341624/b341624.txt">Table of n, a(n) for n = 1..65537</a>

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

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

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A341620(n) = sumdiv(n,d,(sigma(d)>=(2*d)));

%o A341624(n) = { my(t, u=0); while((t=A341620(n))>0, u=t; n = A003961(n)); (u); };

%Y Cf. A005100 (positions of zeros).

%Y Differs from A341620 for the first time at n=120, where a(120)=1, while A341620(120)=8.

%Y Cf. also A341508, A341618.

%K nonn

%O 1,12

%A _Antti Karttunen_, Feb 22 2021