cp's OEIS Frontend

A359545 Numbers that eventually reach zero when iterated with the arithmetic derivative (i.e., are in A099308), but some of their proper divisors will never reach it.

%I A359545 #11 Feb 11 2023 08:10:00
%S A359545 30,70,78,105,126,130,138,150,165,174,182,222,238,246,255,258,266,273,
%T A359545 282,285,286,306,310,315,318,333,338,342,345,350,357,366,369,370,375,
%U A359545 385,390,399,402,414,426,430,442,455,465,474,483,490,494,495,498,510,518,530,546,549,550,555,561,570,574,575
%N A359545 Numbers that eventually reach zero when iterated with the arithmetic derivative (i.e., are in A099308), but some of their proper divisors will never reach it.
%C A359545 Numbers k for which A341999(k) is zero but A359542(k) is not zero.
%C A359545 Any such a nonreaching proper divisor must be one of the terms of A359547.
%e A359545 30 = 2*3*5 is included in this sequence, as although it is in A099308, it is not included in A359544 because its proper divisor 15 is not in A099308. Note that 15 is a term of A359547.
%o A359545 (PARI)
%o A359545 A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));
%o A359545 A341999(n) = if(!n,n,while(n>1, n = A003415checked(n)); (!n));
%o A359545 A359542(n) = sumdiv(n,d,A341999(d));
%o A359545 isA359545(n) = ((0==A341999(n))&&(A359542(n)>0));
%Y A359545 Setwise difference A099308 \ A359544.
%Y A359545 Cf. A003415, A341999, A359542, A359547.
%K A359545 nonn
%O A359545 1,1
%A A359545 _Antti Karttunen_, Jan 05 2023