A246261 Numbers n such that A003961(n) is of the form 4k+1.

1, 3, 4, 9, 10, 11, 12, 13, 14, 16, 23, 25, 27, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 42, 44, 47, 48, 49, 52, 56, 58, 59, 64, 69, 71, 75, 81, 82, 83, 85, 86, 89, 90, 92, 93, 95, 97, 99, 100, 102, 105, 106, 107, 108, 109, 110, 111, 114, 117, 119, 120, 121, 122, 124, 126, 130, 131, 132, 133, 134, 136, 139, 140, 141, 143, 144

Offset: 1

Author

Antti Karttunen, Aug 21 2014

Keywords

• nonn

Comments

Equally: numbers n for which A048673(n) is odd.

Also, after 1, numbers n for which A243062(n) is even.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001

Crossrefs

Complement: A246263.

Positions of zeros in A246271.

Inverse function: A246262.

The first row of array A246259.

Cf. A003961, A048673, A243062, A246265.

Programs

Mathematica

{1}~Join~Select[Range[144], Mod[Times @@ Map[NextPrime[#1]^#2 & @@ # &, FactorInteger[#]], 4] == 1 &] (* Michael De Vlieger, Mar 12 2021 *)

Python

from sympy import factorint, prime, primepi
from operator import mul
def a003961(n):
    f=factorint(n)
    return 1 if n==1 else reduce(mul, [prime(primepi(i) + 1)**f[i] for i in f])
print([n for n in range(1, 201) if a003961(n)%4==1]) # Indranil Ghosh, Jun 12 2017

Formula

For all n >= 1, A246262(a(n)) = n.