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

1,1

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.

Links

Table of n, a(n) for n=1..62.

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.

Cf. A003415, A341999, A359542, A359547.

Sequence in context: A154055 A270758 A241192 * A064623 A112343 A182996

Adjacent sequences: A359542 A359543 A359544 * A359546 A359547 A359548

Keyword

nonn

Author

Antti Karttunen, Jan 05 2023

Status

approved