A358215 Numbers k for which there is no prime p such that p^p divides the arithmetic derivative of k, A003415(k).

2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 17, 18, 19, 21, 22, 23, 25, 26, 29, 30, 31, 33, 34, 37, 38, 41, 42, 43, 45, 46, 47, 49, 50, 53, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 82, 83, 85, 86, 89, 90, 93, 94, 97, 98, 99, 101, 102, 103, 105, 106, 107, 109, 110, 113, 114, 117, 118, 121, 122, 125

Offset: 1

Author

Antti Karttunen, Nov 24 2022

Keywords

• nonn

Comments

Numbers k such that A003415(k) is in A048103.

Links

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

Crossrefs

Complement of {1} U A327929. Positions of 0's in A341996 (after the two initial zeros). Positions of 1's in A341997.

Subsequence of A048103.

Subsequences: A099308 (apart from its two initial terms), A328393, A358221.

Cf. A003415, A327934, A351088, A359550, A368915 (characteristic function).

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]A368915(n) = ((n>1)&&A359550(A003415(n)));
isA358215(n) = A368915(n);