A358232 -id:A358232 - cp's OEIS frontend

A328382 a(n) = A276086(n) mod A003415(n), where A276086 is the primorial base exp-function and A003415 is the arithmetic derivative.

0, 0, 1, 0, 0, 0, 3, 0, 3, 0, 9, 0, 3, 6, 1, 0, 20, 0, 15, 0, 7, 0, 9, 0, 0, 24, 25, 0, 7, 0, 21, 0, 6, 6, 35, 0, 0, 2, 43, 0, 11, 0, 45, 36, 0, 0, 91, 0, 15, 10, 35, 0, 1, 14, 61, 4, 5, 0, 49, 0, 15, 39, 57, 0, 1, 0, 15, 14, 22, 0, 133, 0, 9, 35, 65, 0, 19, 0, 71, 30, 42, 0, 121, 2, 30, 6, 105, 0, 97, 6, 69, 18, 0, 6, 83, 0, 63, 15, 35, 0, 21

Offset: 2

Antti Karttunen, Oct 15 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 2..30030
Index entries for sequences related to primorial base

Cf. A003415, A276086, A327858, A358220, A358221 (positions of 0's), A358232 (of 1's), A358228 (of odd terms), A358229 (of even terms), A358227 (parity of terms).

Cf. also A328386.

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); };
A328382(n) = (A276086(n)%A003415(n));

a(n) = A276086(n) mod A003415(n).

For n >= 2, gcd(a(n), A003415(n)) = A327858(n).

A358228 Numbers k such that A276086(k) mod A003415(k) is an odd number, where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

Original entry on oeis.org

4, 8, 10, 12, 14, 16, 20, 22, 24, 28, 30, 32, 36, 40, 42, 44, 48, 50, 52, 54, 56, 58, 60, 62, 63, 64, 66, 68, 72, 74, 75, 76, 78, 80, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 108, 110, 112, 114, 116, 120, 122, 124, 126, 128, 132, 136, 138, 140, 144, 148, 150, 152, 154, 156, 158, 160, 162, 164, 168, 171, 172, 176

Offset: 1

Antti Karttunen, Nov 25 2022

nonn

Index entries for sequences related to primorial base

Complement: {1} U A358229.
Cf. A003415, A276086, A328382, A358228 (characteristic function), A358232 (subsequence).
Cf. also A358225.

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); };
A358227(n) = ((A276086(n)%A003415(n))%2);
isA358228(n) = A358227(n);

cp's OEIS Frontend

A328382 a(n) = A276086(n) mod A003415(n), where A276086 is the primorial base exp-function and A003415 is the arithmetic derivative.

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