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

1,2

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

Cf. A135772-A135779, A095862.

Sequence in context: A290729 A314295 A288155 * A353686 A219016 A348753

Adjacent sequences: A135772 A135773 A135774 * A135776 A135777 A135778

Keyword

base,nonn

Author

M. F. Hasler, Nov 28 2007

Status

approved