A353485 - OEIS

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

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OFFSET

1,2

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

PROG

(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); };

CROSSREFS

Positions of zeros in A353484.

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

Subsequence of A001694.