A373373 - OEIS

A373373

Numbers k for which both A001414(k) and A276085(k) are multiples of 3, where A001414 is the sum of prime factors with repetition and A276085 is the primorial base log-function.

%I #10 Jun 04 2024 14:24:19

%S 1,8,27,35,42,64,65,77,78,95,114,119,125,143,150,155,161,180,185,186,

%T 203,209,215,216,221,222,258,275,280,287,299,305,323,329,330,335,336,

%U 341,343,365,366,371,377,395,396,402,407,413,425,437,438,473,474,485,497,510,512,515,520,527,533,545,551,575,581,582

%N Numbers k for which both A001414(k) and A276085(k) are multiples of 3, where A001414 is the sum of prime factors with repetition and A276085 is the primorial base log-function.

%C As A001414 and A276085 are both fully additive, this sequence forms a multiplicative semigroup: if m and n are in the sequence, then so is m*n.

%H Antti Karttunen, <a href="/A373373/b373373.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) isA373373 = A373372;

%Y Cf. A001414, A276085, A373372 (characteristic function).

%Y Intersection of A289142 and A339746.

%Y Positions of multiples of 3 in A373362.

%Y Cf. also A373144.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 02 2024