OFFSET
1,1
COMMENTS
Numbers of the form n = m*p^p (where p is prime), i.e., multiples of some term in A051674, have n' = (m + m')*p^p, which is again of the same form, but strictly larger iff m > 1. Therefore successive derivatives grow to infinity in this case, and they are constant when m = 1. There are other terms in this sequence, but I conjecture that they all eventually lead to a term of this form, e.g., 26 -> 15 -> 8 etc. - M. F. Hasler, Apr 09 2015
REFERENCES
See A003415.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
PROG
(PARI) is(n)=until(4>n=factorback(n~)*sum(i=1, #n, n[2, i]/n[1, i]), for(i=1, #n=factor(n)~, n[1, i]>n[2, i]||return(1))) \\ M. F. Hasler, Apr 09 2015
CROSSREFS
Cf. A003415 (arithmetic derivative of n), A099307 (least k such that the k-th arithmetic derivative of n is zero), A099308 (numbers whose k-th arithmetic derivative is zero for some k).
Cf. A341999 (characteristic function),
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 12 2004
STATUS
approved