login
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.
3
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
1,1
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.
EXAMPLE
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.
PROG
(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));
CROSSREFS
Setwise difference A099308 \ A359544.
Sequence in context: A154055 A270758 A241192 * A064623 A112343 A182996
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 05 2023
STATUS
approved