A135775 Numbers having number of divisors equal to number of digits in base 5.

1, 5, 7, 11, 13, 17, 19, 23, 25, 49, 121, 125, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 177, 178, 183, 185, 187, 194, 201, 202, 203, 205, 206, 209, 213, 214, 215, 217, 218, 219, 221, 226, 235, 237, 247, 249, 253, 254, 259, 262, 265, 267

Offset: 1

Author

M. F. Hasler, Nov 28 2007

Keywords

• base
• nonn

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.

Examples

			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.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A135772-A135779, A095862.

Programs

Mathematica

Select[Range[300],DivisorSigma[0,#]==IntegerLength[#,5]&] (* Harvey P. Dale, Mar 14 2013 *)

PARI

for(d=1,4,for(n=5^(d-1),5^d-1,d==numdiv(n)&print1(n", ")))