A353485 Numbers k such that no x with an odd arithmetic derivative is encountered when repeatedly prime shifting from k down to 1 with the map x -> A064989(x).

1, 4, 8, 9, 16, 25, 32, 36, 49, 64, 72, 81, 100, 108, 121, 128, 144, 169, 196, 200, 216, 225, 256, 288, 289, 324, 361, 392, 400, 432, 441, 484, 512, 529, 576, 625, 648, 676, 729, 784, 800, 841, 864, 900, 961, 968, 972, 1024, 1089, 1152, 1156, 1225, 1296, 1352, 1369, 1444, 1521, 1568, 1600, 1681, 1728, 1764, 1800, 1849

Offset: 1

Author

Antti Karttunen, Apr 23 2022

Keywords

• nonn

Comments

Note that k itself must also be in A235992 to be included here. All terms must be powerful (in A001694) because otherwise at some point in the shifting process a number of the form 4u+2 would be encountered, and they are all in A235991.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Positions of zeros in A353484.

Cf. A000290 (subsequence), A003415, A064989, A165560, A235991, A235992.

Subsequence of A001694.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A064989(n) = { my(f=factor(A000265(n))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
isA353485(n) = { while(n>1, if(A003415(n)%2, return(0)); n = A064989(n)); (1); };