A285710 Numbers n for which A000010(n) = A285699(n); positions of zeros in A285709.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 16, 17, 19, 21, 23, 25, 27, 28, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 62, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 124, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 237

Offset: 1

Author

Antti Karttunen, Apr 26 2017

Keywords

• nonn

Comments

After a(1) = 1, also numbers n such that A051953(n) = A079277(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..6672

Crossrefs

Positions of zeros in A285709.

Cf. A000010, A051953, A079277, A208815, A285699.

Cf. A000961 (a subsequence).

Programs

Mathematica

Flatten@ Position[#, 0] &@ Table[EulerPhi@ n - (n - If[n <= 2, n - 1, Module[{k = n - 2, e = Floor@ Log2@ n}, While[PowerMod[n, e, k] != 0, k--]; k]]), {n, 240}] (* Michael De Vlieger, Apr 26 2017 *)

Python

from sympy import divisors, totient
from sympy.ntheory.factor_ import core
def a007947(n): return max(i for i in divisors(n) if core(i) == i)
def a079277(n):
    k=n - 1
    while True:
        if a007947(k*n) == a007947(n): return k
        else: k-=1
def a285699(n): return 1 if n<2 else n - a079277(n)
print([n for n in range(1, 301) if totient(n) == a285699(n)]) # Indranil Ghosh, Apr 26 2017