OFFSET
1,2
COMMENTS
Since 5 is a prime, any power 5^k has k+1 divisors { 5^i ; i=0..k } and the same number of digits in base 5; thus the sequence A000351(k)=5^k is a subsequence of this one. It also includes the powers of 7 up to 7^4, since (7/5)^4 < 5 < (7/5)^5.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
EXAMPLE
a(1) = 1 since 1 has 1 divisor and 1 digit (in base 5).
2,3,4 have 2 resp. 3 divisors but only 1 digit in base 5, so they are not members of the sequence.
a(2) = 5 = 10_5 has 2 divisors { 1, 5 } and 2 digits in base 5, so it is (the second term) in this sequence.
MATHEMATICA
Select[Range[300], DivisorSigma[0, #]==IntegerLength[#, 5]&] (* Harvey P. Dale, Mar 14 2013 *)
PROG
(PARI) for(d=1, 4, for(n=5^(d-1), 5^d-1, d==numdiv(n)&print1(n", ")))
CROSSREFS
KEYWORD
base,nonn
AUTHOR
M. F. Hasler, Nov 28 2007
STATUS
approved