A276079 Numbers n such that prime(k)^(k+1) divides n for some k.

4, 8, 12, 16, 20, 24, 27, 28, 32, 36, 40, 44, 48, 52, 54, 56, 60, 64, 68, 72, 76, 80, 81, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 135, 136, 140, 144, 148, 152, 156, 160, 162, 164, 168, 172, 176, 180, 184, 188, 189, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232, 236, 240, 243, 244, 248, 252, 256, 260, 264, 268, 270, 272

Offset

1,1

Comments

The asymptotic density of this sequence is 1 - Product_{i>=1} 1-prime(i)^(-1-i) = 0.2789766... - Amiram Eldar, Oct 21 2020

Links

Antti Karttunen, Table of n, a(n) for n = 1..5000

Example

625 = 5*5*5*5 = prime(3)^4 so it is divisible by prime(3)^(3+1), and thus 625 is included in the sequence.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A276079 (NONZERO-POS 1 1 A276077))
(Python)
from sympy import primepi, isprime, primefactors, factorint
def a028234(n):
    f=factorint(n)
    minf = min(f)
    return 1 if n==1 else n//(minf**f[minf])
def a067029(n):
    f=factorint(n)
    return 0 if n==1 else f[min(f)]
def a049084(n): return primepi(n) if isprime(n) else 0
def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))
def a(n): return 0 if n==1 else a(a028234(n)) + (1 if a067029(n) > a055396(n) else 0)
print([n for n in range(1, 301) if a(n)!=0]) # Indranil Ghosh, Jun 21 2017

Crossrefs

Positions of nonzeros in A276077.

Complement: A276078.

Cf. A000040, A000720, A008586 (a subsequence).

Differs from its subsequence A100716 for the first time at n=175, where a(175) = 625, while that value is missing from A100716.

Sequence in context: A086133 A100716 A328251 * A311124 A191677 A076310

Adjacent sequences: A276076 A276077 A276078 * A276080 A276081 A276082

Keyword

nonn

Author

Antti Karttunen, Aug 18 2016

Status

approved