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.

30, 70, 78, 105, 126, 130, 138, 150, 165, 174, 182, 222, 238, 246, 255, 258, 266, 273, 282, 285, 286, 306, 310, 315, 318, 333, 338, 342, 345, 350, 357, 366, 369, 370, 375, 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

Offset: 1

Author

Antti Karttunen, Jan 05 2023

Keywords

• nonn

Comments

Numbers k for which A341999(k) is zero but A359542(k) is not zero.

Any such a nonreaching proper divisor must be one of the terms of A359547.

Examples

			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.
		

Crossrefs

Setwise difference A099308 \ A359544.

Cf. A003415, A341999, A359542, A359547.

Programs

PARI

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));
A341999(n) = if(!n,n,while(n>1, n = A003415checked(n)); (!n));
A359542(n) = sumdiv(n,d,A341999(d));
isA359545(n) = ((0==A341999(n))&&(A359542(n)>0));