A392594 - OEIS

A392594

Numbers k such that A003415(k) == A276085(k) (mod 4), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function.

1, 2, 10, 12, 15, 16, 18, 20, 26, 28, 34, 35, 39, 42, 44, 50, 51, 52, 55, 58, 66, 68, 74, 76, 81, 82, 87, 90, 91, 92, 95, 98, 106, 108, 111, 114, 115, 116, 119, 122, 123, 124, 130, 138, 143, 144, 146, 148, 154, 155, 159, 162, 164, 170, 172, 178, 180, 183, 186, 187, 188, 189, 192, 194, 202, 203, 210, 212, 215, 218

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The sequence is the disjoint union of the following sequences:

A360110 - odd k such that A003415(k) == A276085(k) == 0 (mod 4).

A369668 - k with A001222(k) = even and k' = 4m+3, all are of the form 8m+2,

2*A359161 - k with A001222(k) = odd and k' = 4m+1, all are of the form 8m+2,

4*A373142 - even k such that A003415(k) == A276085(k) == 0 (mod 4).

Sequence contains all the terms of A017089, which is the union of 2*A359161 and 2*A359151 (= A369668), but none of the terms of A017137. See also comments in A369650.

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]));

A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); };

is_A392594(n) = !((A276085(n)-A003415(n))%4);

CROSSREFS

Cf. A001222, A003415, A017137, A276085, A359151, A359161, A369001, A369002.

Subsequences: A017089, A360110 (odd terms), A369650, A369668, 4*A373142 (the terms that are multiples of 4).

Cf. also A392593.

Sequence in context: A349831 A079252 A108064 * A057989 A050978 A053449