A336917 Number of iterations of x -> A252463(x) needed before the result is deficient, when starting from x=n.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 1, 0, 1, 0, 1, 0

Offset

1,12

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

For all n >= 0, a(A007283(n)) = n.

Example

For n = 945, the first odd abundant number, the iteration of A252463 proceeds as 945 -> 120 -> 60 -> 30 -> 15 -> 6 -> 3 -> 2 -> 1. From 945 to 30, all are nondeficient (sigma(k) >= 2k), and only at 15 we encounter the first deficient number, as sigma(15) = 24 < 2*15. Therefore a(945) = 4.

Prog

(PARI)
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A252463(n) = if(!(n%2), n/2, A064989(n));
A336917(n) = { my(i=0); while(sigma(n) >= (2*n), n = A252463(n); i++); (i); };

Crossrefs

Cf. A005100, A007283, A023196, A064989, A252463, A294934, A336389, A336834, A336835, A336915.

Sequence in context: A321379 A070141 A088722 * A122180 A363742 A033772

Adjacent sequences: A336914 A336915 A336916 * A336918 A336919 A336920

Keyword

nonn

Author

Antti Karttunen, Aug 08 2020

Status

approved