A341618 a(n) = 0 if n is not a primitive nondeficient number, otherwise a(n) is the number of primitive nondeficient divisors of the last number in the iteration x -> A003961(x) (starting from x=n) for which that count (A337690) is nonzero.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Antti Karttunen, Feb 21 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Differs from A337690 for the first time at n=120, where a(120)=1, while A337690(120)=2.

Cf. A006039, A341508, A341619, A341624.

Programs

PARI

A341619(n) = if(sigma(n) < (2*n), 0, fordiv(n, d, if((d= 2*d), return(0))); (1)); \\ After code in A071395
A337690(n) = sumdiv(n,d,A341619(d));
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A341618(n) = { my(t, u=0); while((t=A337690(n))>0, u=t; n = A003961(n)); (u); };