A358231 -id:A358231 - cp's OEIS frontend

A328387 Numbers k such that A276086(k) is a multiple of k.

1, 3, 15, 25, 75, 105, 147, 175, 343, 385, 525, 539, 625, 735, 825, 1029, 1155, 1225, 1331, 1375, 1617, 1815, 2695, 3003, 3025, 3675, 3773, 3993, 4375, 5005, 5145, 5577, 5775, 6655, 6825, 8085, 8125, 8281, 8575, 9075, 9555, 9625, 10725, 11011, 11319, 12675, 12705, 13013, 13377, 15015, 15379, 15925, 17303, 17745, 17787, 17875

Offset: 1

Antti Karttunen, Oct 15 2019

nonn

All terms are odd. Of the first 3003 terms, 1709 are multiples of five.

Antti Karttunen, Table of n, a(n) for n = 1..3003

Cf. A276086, A324198.
Indices of 0's in A328386. Indices of 1's in A351250.
Subsequence of A048103 and of A358226.
Cf. also A370114, A358231.

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA328387(n) = (0==(A276086(n)%n));

A358225 Numbers k such that A276086(k) mod k is an odd number, where A276086 is the primorial base exp-function.

Original entry on oeis.org

2, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 16, 18, 19, 20, 21, 22, 23, 24, 26, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 58, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 76, 78, 79, 80, 81, 82, 84, 86, 88, 89, 90, 91, 92, 94, 96, 97, 98, 99, 100, 101

Offset: 1

Antti Karttunen, Nov 25 2022

nonn

Index entries for sequences related to primorial base

Cf. A000035, A005843 (subsequence after 0), A276086, A328386, A358225 (characteristic function), A358226 (complement), A358231 (subsequence).

Cf. also A358228.

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A358224(n) = ((A276086(n)%n)%2);
isA358225(n) = A358224(n);

{k | A328386(k) == 1 (mod 2)}.

A358232 Numbers k for which A276086(k) == 1 mod A003415(k), where A276086 is the primorial base exp-function, and A003415 is the arithmetic derivative.

Original entry on oeis.org

4, 16, 54, 66, 864, 1710, 18900, 71254, 120731, 492943, 625081, 700149, 1489459, 3564419, 44995876, 219794251, 297776323, 596506003, 642171139, 972082711, 1065608507, 1252704562, 1385872853, 1416187590, 1799971549, 1818740449

Offset: 1

Antti Karttunen, Nov 25 2022

nonn

Index entries for sequences related to primorial base

Subsequence of A358228. Positions of 1's in A328382.
Cf. A003415, A276086.
Cf. also A358231.

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); };
isA358232(n) = (1==(A276086(n)%A003415(n)));

cp's OEIS Frontend

A328387 Numbers k such that A276086(k) is a multiple of k.

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A358225 Numbers k such that A276086(k) mod k is an odd number, where A276086 is the primorial base exp-function.

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A358232 Numbers k for which A276086(k) == 1 mod A003415(k), where A276086 is the primorial base exp-function, and A003415 is the arithmetic derivative.

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