Kevin Foote - cp's OEIS frontend

User: Kevin Foote

Kevin Foote has authored 2 sequences.

A334395 Partial products of A334393.

1, 2, 6, 24, 120, 840, 6720, 60480, 665280, 8648640, 147026880, 2793510720, 64250746560, 1606268664000, 43369253928000, 1257708363912000, 38988959281272000, 1247646697000704000, 46162927789026048000, 1892680039350067968000, 81385241692052922624000

Offset: 1

Kevin Foote, Apr 26 2020

nonn

			a(6) = 1*2*3*4*5*7 = 840.

Amiram Eldar, Table of n, a(n) for n = 1..358

Cf. A008578, A024923, A334393.

Rest @ FoldList[Times, 1, Select[Range[43], Length[(f = FactorInteger[#])] == 1 && ((e = f[[1, 2]]) == 1 || PrimeQ[e]) &]] (* Amiram Eldar, May 11 2020 *)

isok(n) = if (n==1, return (1)); my(k=isprimepower(n)); (k==1) || isprime(k); \\ A334393
lista(nn) = {my(v = select(x->isok(x), [1..nn]), p=1); for (n=1, #v, p *= v[n]; print1(p, ", "););} \\ Michel Marcus, May 11 2020

a(n) = Product_{i=1..n} A334393(i).

A334393 Numbers of the form p^q where p and q are either 1 or prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 251

Offset: 1

Kevin Foote, Apr 26 2020

nonn

First differs from A115975 at a(42). - Omar E. Pol, Apr 26 2020

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..218 from Kevin Foote)

Union of A008578 and A053810.

Cf. A115975.

Select[Range[250], Length[(f = FactorInteger[#])] == 1 && ((e = f[[1, 2]]) == 1 || PrimeQ[e]) &] (* Amiram Eldar, Apr 27 2020 *)

isok(n) = if (n==1, return (1)); my(k=isprimepower(n)); (k==1) || isprime(k); \\ Michel Marcus, Apr 27 2020

from sympy import primepi, integer_nthroot, primerange
def A334393(n):
    def f(x): return int(n-1+x-primepi(x)-sum(primepi(integer_nthroot(x, p)[0]) for p in primerange(x.bit_length())))
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return m # Chai Wah Wu, Aug 13 2024

cp's OEIS Frontend

User: Kevin Foote

A334395 Partial products of A334393.

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