A356305 -id:A356305 - cp's OEIS frontend

A356311 Numbers k for which A003415(k) and A276086(k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

0, 2, 3, 4, 5, 7, 10, 11, 12, 13, 16, 17, 18, 19, 22, 23, 24, 28, 29, 30, 31, 32, 34, 37, 40, 41, 42, 43, 47, 53, 54, 56, 58, 59, 60, 61, 66, 67, 70, 71, 72, 73, 78, 79, 80, 82, 83, 84, 89, 90, 96, 97, 101, 103, 104, 105, 107, 108, 109, 113, 114, 118, 120, 124, 127, 130, 131, 132, 136, 137, 138, 139, 140, 142, 144

Offset: 1

Antti Karttunen, Nov 03 2022

nonn

Index entries for sequences related to primorial base

Positions of 1's in A327858. Positions of 0's in A356304 (for n >= 2) and in A356305.
Cf. A003415, A276086, A356310 (characteristic function), A356312 (complement).
Cf. also A324583.

isA356311(n) = A356310(n); \\ See code in A356310.

A356303 The least k >= 0 such that n and A276086(n-k) are relatively prime, where A276086 is the primorial base exp-function.

Original entry on oeis.org

0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 14, 0, 0, 0, 0, 16, 2, 0, 0, 0, 20, 0, 2, 0, 0, 0, 0, 0, 2, 0, 30, 0, 0, 0, 2, 6, 0, 18, 0, 0, 14, 0, 0, 0, 20, 16, 2, 0, 0, 0, 20, 28, 2, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 2, 66, 0, 0, 0, 0, 14, 0, 48, 0, 0, 16, 2, 0, 0, 60, 20, 0, 2, 0, 0, 0, 62, 0, 2, 0, 0, 0, 0, 70, 2, 6

Offset: 0

Antti Karttunen, Nov 03 2022

All terms are even.

Antti Karttunen, Table of n, a(n) for n = 0..11550
Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
Antti Karttunen, Scatter plot up to n=65537
Index entries for sequences related to primorial base

Cf. A276086, A324198.
Cf. A324583 (positions of zeros).
Cf. also A356302, A356305.

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A356303(n) = { my(k=0); while(gcd(A276086(n-k),n)!=1,k++); (k); };

A356304 The least k >= 0 such that A003415(n) and A276086(n+k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

Original entry on oeis.org

0, 0, 0, 0, 24, 0, 4, 3, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 4, 9, 0, 0, 0, 5, 4, 3, 0, 0, 0, 0, 0, 177, 0, 1, 24, 0, 172, 1, 0, 0, 0, 0, 4, 3, 14, 0, 162, 161, 10, 9, 158, 0, 0, 1, 0, 1, 0, 0, 0, 0, 4, 3, 2, 1, 0, 0, 4, 1, 0, 0, 0, 0, 4, 15, 14, 1, 0, 0, 0, 3, 0, 0, 0, 1, 4, 1, 122, 0, 0, 1, 4, 1, 116, 1, 0, 0, 2212, 21

Offset: 2

Antti Karttunen, Nov 03 2022

nonn

Antti Karttunen, Table of n, a(n) for n = 2..11550
Antti Karttunen, Data supplement: n, a(n) computed for n = 2..65537
Index entries for sequences related to primorial base

Cf. A003415, A276086, A356311 (after its initial zero gives the positions of zeros in this sequence).

Cf. also A356302, A356305.

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A356304(n) = { my(k=0,x=A003415(n)); while(gcd(A276086(n+k),x)!=1,k++); (k); };

cp's OEIS Frontend

A356311 Numbers k for which A003415(k) and A276086(k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

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A356303 The least k >= 0 such that n and A276086(n-k) are relatively prime, where A276086 is the primorial base exp-function.

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A356304 The least k >= 0 such that A003415(n) and A276086(n+k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

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PARI