A135773 Numbers having number of divisors equal to number of digits in base 3.

1, 3, 5, 7, 9, 25, 27, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 81, 243, 244, 245, 261, 268, 275, 279, 284, 292, 316, 325, 332, 333, 338, 356, 363, 369, 387, 388, 404, 412, 423, 425, 428, 436, 452, 475, 477, 507, 508, 524, 531, 539, 548, 549

Offset

1,2

Comments

Since 3 is a prime, any power 3^k has k+1 divisors { 3^i ; i=0..k } and the same number of digits in base 3; thus the sequence A000244(k) = 3^k is a subsequence of this one. Note that no number in between 3^4 and 3^5, neither in between 3^6 and 3^7, is in this sequence.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1250

Example

a(1) = 1 since 1 has 1 divisor and 1 digit (in base 3).
2 has 2 divisors but only 1 digit in base 3, so it is not member of the sequence.
a(2)..a(4) = 3, 5, 7 all have 2 divisors and 2 digits in base 3.
81 = 3^4 = 10000_3 is the only number with 5 divisors and 5 digits in base 3, so it is followed by 243 = 3^5 = 100000_3.

Mathematica

Select[Range[500], DivisorSigma[0, #] == IntegerLength[#, 3] &] (* G. C. Greubel, Nov 08 2016 *)

Prog

(PARI) for(d=1, 6, for(n=3^(d-1), 3^d-1, d==numdiv(n)&print1(n", ")))

Crossrefs

Cf. A135772 - A135779, A095862.

Sequence in context: A329364 A100028 A053681 * A357677 A262029 A259380

Adjacent sequences: A135770 A135771 A135772 * A135774 A135775 A135776

Keyword

base,nonn

Author

M. F. Hasler, Nov 28 2007

Status

approved