cp's OEIS Frontend

A351959 Composite k such that the primorial inflation of k is a sum of distinct primorial numbers.

%I A351959 #15 Apr 06 2022 18:14:39
%S A351959 8,9,27,32,40,42,115,228,252,530,575,928,1032,1206,2595,5300,5726,
%T A351959 9320,10590,14464,17376,21708,22734,23212,25267,26229,37360,38925,
%U A351959 42540,72768,80164,92772,171960,220045,277937,325152,372800,374864,390169,404475,405988,417798,421932,456753,475587,686640
%N A351959 Composite k such that the primorial inflation of k is a sum of distinct primorial numbers.
%C A351959 Composite numbers k for which A108951(k) is in A276156.
%C A351959 Numbers k for which A324886(k) is a nonprime squarefree number (in A120944).
%C A351959 Question: Is A324886(k) always a semiprime, or could it have more than two distinct prime factors?
%H A351959 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A351959 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%e A351959 For the initial 14 terms, k and A049345(A108951(k)) are listed below:
%e A351959      8 -> 110,
%e A351959      9 -> 1100,
%e A351959     27 -> 10100,
%e A351959     32 -> 1010,
%e A351959     40 -> 11000,
%e A351959     42 -> 110000,
%e A351959    115 -> 11000000000,
%e A351959    228 -> 1100000000,
%e A351959    252 -> 1010000,
%e A351959    530 -> 110000000000000000,
%e A351959    575 -> 101000000000,
%e A351959    928 -> 110000000000,
%e A351959   1032 -> 1100000000000000,
%e A351959   1206 -> 110000000000000000000.
%o A351959 (PARI)
%o A351959 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A351959 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
%o A351959 is_in_A276156(n) = { my(p=2); while(n, if((n%p)>1,return(0)); n = n\p; p = nextprime(1+p)); (1); };
%o A351959 isA351959(n) =  (n>1 && !isprime(n) && is_in_A276156(A108951(n)));
%Y A351959 Intersection of A002808 and A344591.
%Y A351959 Cf. A049345, A108951, A120944, A276156, A324886, A351957.
%K A351959 nonn
%O A351959 1,1
%A A351959 _Antti Karttunen_, Apr 05 2022