A135773 - OEIS

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

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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