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

1,1

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).

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to factorial base representation

Example

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.

Prog

(Scheme, with Antti Karttunen's IntSeq-library, two alternatives)
(define A275805 (ZERO-POS 1 1 (COMPOSE A008683 A275734)))
(define A275805 (MATCHING-POS 1 1 (lambda (n) (< 1 (A275811 n)))))
(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<p else a007623(n//p, p+1)*10 + n%p
def a275732(n):
    x=str(a007623(n))[::-1]
    return 1 if n==0 or "1" not in x else reduce(mul, [prime(i + 1) for i in range(len(x)) if x[i]=='1'])
def a257684(n):
    x=str(a007623(n))[:-1]
    y="".join(str(int(i) - 1) if int(i)>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

Crossrefs

Complement: A275804.

Cf. A007623, A008683, A275734, A275811.

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

Subsequence of A115945.

Sequence in context: A346147 A275118 A275640 * A340605 A313993 A297251

Adjacent sequences: A275802 A275803 A275804 * A275806 A275807 A275808

Keyword

nonn,base

Author

Antti Karttunen, Aug 10 2016

Status

approved