A328392 -id:A328392 - OEIS

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A327860

Arithmetic derivative of the primorial base exp-function: a(n) = A003415(A276086(n)).

+10
79

0, 1, 1, 5, 6, 21, 1, 7, 8, 31, 39, 123, 10, 45, 55, 185, 240, 705, 75, 275, 350, 1075, 1425, 3975, 500, 1625, 2125, 6125, 8250, 22125, 1, 9, 10, 41, 51, 165, 12, 59, 71, 247, 318, 951, 95, 365, 460, 1445, 1905, 5385, 650, 2175, 2825, 8275, 11100, 30075, 4125, 12625, 16750, 46625, 63375, 166125, 14, 77, 91, 329, 420

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A328114

Maximal digit value used when n is written in primorial base (cf. A049345).

+10
54

0, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

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A328389

Maximal digit value in primorial base expansion of A276086(n): a(n) = A328114(A276086(n)).

+10
13

1, 1, 1, 1, 1, 3, 2, 2, 2, 1, 2, 3, 4, 3, 2, 5, 2, 2, 4, 2, 5, 4, 5, 10, 6, 6, 8, 6, 5, 9, 1, 2, 3, 2, 2, 4, 2, 2, 3, 1, 3, 3, 5, 4, 3, 5, 7, 4, 4, 8, 3, 3, 4, 9, 9, 8, 7, 11, 4, 8, 3, 3, 4, 4, 3, 4, 2, 2, 3, 7, 10, 10, 5, 4, 6, 3, 8, 9, 7, 5, 10, 10, 10, 8, 5, 5, 8, 6, 9, 7, 4, 4, 6, 9, 4, 7, 8, 5, 3, 5, 7, 4, 7, 7, 11, 9

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A328391

Maximal exponent in the prime factorization of A327860(n): a(n) = A051903(A327860(n)).

+10
13

0, 0, 1, 1, 1, 0, 1, 3, 1, 1, 1, 1, 2, 1, 1, 4, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 0, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 2, 2, 7, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2

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A328390

Maximal digit value in primorial base expansion of the arithmetic derivative of n: a(n) = A328114(A003415(n)).

+10
11

0, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 4, 2, 2, 1, 2, 2, 2, 4, 1, 1, 1, 1, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 3, 1, 4, 1, 3, 2, 2, 3, 4, 1, 3, 2, 3, 3, 1, 1, 3, 1, 1, 3, 6, 3, 2, 1, 2, 4, 4, 1, 5, 1, 1, 4, 3, 3, 2, 1, 5, 3, 2, 1, 4, 3, 2, 1, 4, 1, 4, 3, 3, 2, 3, 4, 2, 1, 2, 2, 4, 1, 3, 1, 5, 2

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A342005

a(n) = A342004(A276086(n)).

+10
6

1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1

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A328396

Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = A046523(A276086(A003415(A276086(n)))).

+10
4

1, 2, 2, 3, 2, 4, 2, 5, 5, 5, 6, 7, 3, 8, 7, 9, 5, 10, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2, 22, 3, 8, 23, 24, 25, 26, 11, 6, 27, 28, 29, 24, 11, 30, 31, 32, 27, 33, 10, 34, 35, 36, 37, 38, 39, 19, 40, 41, 3, 42, 43, 44, 25, 45, 46, 11, 9, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 4, 69, 70, 71, 72, 73, 74, 32

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