A275805 Indices of nonsquarefree terms in A275734; numbers with at least one digit slope (in their factorial base representation) with multiple nonzero digits. (See comments for the exact definition).

5, 11, 14, 15, 17, 19, 21, 22, 23, 29, 35, 38, 39, 41, 43, 45, 46, 47, 53, 54, 55, 56, 57, 58, 59, 62, 63, 65, 67, 69, 70, 71, 74, 75, 77, 80, 81, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 100, 101, 103, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 125, 131, 134, 135, 137, 139, 141, 142, 143, 149, 155

Offset: 1

Author

Antti Karttunen, Aug 10 2016

Keywords

• nonn
• base

Comments

Numbers n for which A008683(A275734(n)) = 0.

Numbers n for which A275811(n) > 1.

Numbers n in whose factorial base representation (A007623) there exists at least one pair of digit positions i_1 and i_2 with nonzero digits d_1 and d_2 such that (i_1 - d_1) = (i_2 - d_2).

Examples

			For n=5, "21" in factorial base (A007623), the pair 2 (in position 2) and 1 (in position 1) satisfies the condition, as (2-2) = (1-1), thus 5 is included.
For n=55, "2101" in factorial base, the pair 2 (in position 4) and 1 (in position 3) satisfies the condition, as (4-2) = (3-1), thus 55 is included.
For n=67, "2301" in factorial base, the pair 3 (in position 3) and 1 (in position 1) satisfies the condition, as (3-3) = (1-1), thus 67 is included in the sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to factorial base representation

Crossrefs

Complement: A275804.

Cf. A007623, A008683, A275734, A275811.

Cf. A275809 (a subsequence apart from its initial 0-term).

Subsequence of A115945.

Programs

Python

from operator import mul
from sympy import prime, factorial as f, mobius
from functools import reduce
def a007623(n, p=2): return n if n
0 else '0' for i in x)[::-1]
    return 0 if n==1 else sum([int(y[i])*f(i + 1) for i in range(len(y))])
def a(n): return 1 if n==0 else a275732(n)*a(a257684(n))
print([n for n in range(201) if mobius(a(n))==0]) # Indranil Ghosh, Jun 19 2017