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

8, 9, 27, 32, 40, 42, 115, 228, 252, 530, 575, 928, 1032, 1206, 2595, 5300, 5726, 9320, 10590, 14464, 17376, 21708, 22734, 23212, 25267, 26229, 37360, 38925, 42540, 72768, 80164, 92772, 171960, 220045, 277937, 325152, 372800, 374864, 390169, 404475, 405988, 417798, 421932, 456753, 475587, 686640

Offset: 1

Author

Antti Karttunen, Apr 05 2022

Keywords

• nonn

Comments

Composite numbers k for which A108951(k) is in A276156.

Numbers k for which A324886(k) is a nonprime squarefree number (in A120944).

Question: Is A324886(k) always a semiprime, or could it have more than two distinct prime factors?

Examples

			For the initial 14 terms, k and A049345(A108951(k)) are listed below:
     8 -> 110,
     9 -> 1100,
    27 -> 10100,
    32 -> 1010,
    40 -> 11000,
    42 -> 110000,
   115 -> 11000000000,
   228 -> 1100000000,
   252 -> 1010000,
   530 -> 110000000000000000,
   575 -> 101000000000,
   928 -> 110000000000,
  1032 -> 1100000000000000,
  1206 -> 110000000000000000000.
		

Links

• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Intersection of A002808 and A344591.

Cf. A049345, A108951, A120944, A276156, A324886, A351957.

Programs

PARI

A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
is_in_A276156(n) = { my(p=2); while(n, if((n%p)>1,return(0)); n = n\p; p = nextprime(1+p)); (1); };
isA351959(n) =  (n>1 && !isprime(n) && is_in_A276156(A108951(n)));