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

1,1

Comments

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

Links

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

Prog

(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]<f[k, 1])); };
A368915(n) = ((n>1)&&A359550(A003415(n)));
isA358215(n) = A368915(n);

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).

Sequence in context: A305847 A248565 A065896 * A099308 A359544 A074235

Adjacent sequences: A358212 A358213 A358214 * A358216 A358217 A358218

Keyword

nonn

Author

Antti Karttunen, Nov 24 2022

Status

approved