A056808 Members of A055932 which are not least prime signatures (cf. A025487).

18, 54, 90, 108, 150, 162, 270, 300, 324, 450, 486, 540, 600, 630, 648, 750, 810, 972, 1050, 1200, 1350, 1458, 1470, 1500, 1620, 1890, 1944, 2100, 2250, 2400, 2430, 2700, 2916, 2940, 3000, 3150, 3240, 3750, 3780, 3888, 4050, 4200, 4374, 4410, 4500, 4800

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

{a(n) : n >= 1} = {A057335(A335485(k)) : k >= 1}. - Peter Munn, Feb 02 2024

Sum_{n>=1} 1/a(n) = A345974 - A161360 = 0.15229524564163275059... . - Amiram Eldar, Jun 26 2025

Example

18 = 2*3*3 and all prime divisors are consecutive primes but the least prime signature is 12 = 2*2*3; so a(1) = 18.

Mathematica

With[{nn = 4800}, Select[Range[2, nn], And[#1 != Times @@ MapIndexed[Prime[First@ #2]^#1 &, Sort[#3, Greater]], Last[#2] == Prime@ Length[#2]] & @@ Apply[Join, {{#1}, Transpose@ #2}] & @@ {#, FactorInteger[#]} &] ] (* Michael De Vlieger, Feb 06 2020 *)

Prog

(Python)
from itertools import count
from functools import lru_cache
from sympy import prime, integer_log, primorial
from oeis_sequences.OEISsequences import bisection
def A056808(n):
    @lru_cache(maxsize=None)
    def g(x, m, j): return sum(g(x//(prime(m)**i), m-1, i) for i in range(j, integer_log(x, prime(m))[0]+1)) if m-1 else max(0, x.bit_length()-j)
    @lru_cache(maxsize=None)
    def h(x, m): return sum(h(x//(prime(m)**i), m-1) for i in range(1, integer_log(x, prime(m))[0]+1)) if m-1 else x.bit_length()-1
    def f(x):
        c = n+x
        for k in count(1):
            if primorial(k)>x:
                break
            c -= h(x, k)-g(x, k, 1)
        return c
    return bisection(f, n, n) # Chai Wah Wu, Mar 23 2026

Crossrefs

Cf. A025487, A055932, A057335, A161360, A335485, A345974.

Sequence in context: A068396 A205874 A044120 * A044501 A386224 A163758

Adjacent sequences: A056805 A056806 A056807 * A056809 A056810 A056811

Keyword

easy,nonn

Author

Alford Arnold, Aug 22 2000

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Nov 28 2000

Status

approved