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

1,1

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?

Links

Table of n, a(n) for n=1..46.

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

Example

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.

Prog

(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)));

Crossrefs

Intersection of A002808 and A344591.

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

Sequence in context: A042311 A003997 A114090 * A217843 A139753 A046874

Adjacent sequences: A351956 A351957 A351958 * A351960 A351961 A351962

Keyword

nonn

Author

Antti Karttunen, Apr 05 2022

Status

approved