OFFSET
1,2
COMMENTS
Since 7 is a prime, any power 7^k has k+1 divisors { 7^i ; i=0..k } and the same number of digits in base 7; thus the sequence A000420(k)=7^k is a subsequence of this one.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1250
Abel Jansma, E_8 Symmetry Structures in the Ising model, Master's thesis, University of Amsterdam, 2018.
EXAMPLE
a(1) = 1 since 1 has 1 divisor and 1 digit (in base 7 as in any other base).
All other numbers have at least 2 divisors so there are no other members of the sequence below a(2) = 7 = 10_7 having 2 divisors { 1, 7 } and 2 digits in base 7.
MATHEMATICA
Select[Range[500], DivisorSigma[0, #]==IntegerLength[#, 7]&] (* Harvey P. Dale, Feb 14 2015 *)
PROG
(PARI) for(d=1, 4, for(n=7^(d-1), 7^d-1, d==numdiv(n)&print1(n", ")))
CROSSREFS
KEYWORD
base,nonn
AUTHOR
M. F. Hasler, Nov 28 2007
STATUS
approved