A216395 Number of values of k for which sigma(k) is a permutation of decimal digits of k, for 2^(n-1) < k < 2^n.

1, 0, 0, 0, 0, 0, 1, 0, 3, 2, 0, 6, 3, 5, 14, 22, 26, 60, 64, 71, 179, 333, 274, 751, 1653, 1726, 3032

Offset: 1

Author

V. Raman, Sep 06 2012

Keywords

• nonn
• base
• more

Examples

			a(12) = 6 because the values of k satisfying the condition for 2^11 < k < 2^12 are {2391, 2556, 2931, 3409, 3678, 3679}. - _V. Raman_, Feb 19 2014
		

Crossrefs

Cf. A115920, A000203.

Programs

PARI

a(n)=sum(k=2^(n-1), 2^n, vecsort(digits(k)) == vecsort(digits(sigma(k)))) \\ V. Raman, Feb 19 2014, based on edits by M. F. Hasler

Python

from sympy import divisor_sigma
def A216395(n):
    if n == 1:
        return 1
    c = 0
    for i in range(2**(n-1)+1, 2**n):
        s1, s2 = sorted(str(i)), sorted(str(divisor_sigma(i)))
        if len(s1) == len(s2) and s1 == s2:
            c += 1
    return c # Chai Wah Wu, Jul 23 2015

Formula

a(n) = # { k in A115920 | 2^(n-1) < k < 2^n }. - M. F. Hasler, Feb 24 2014