A135777 Numbers having number of divisors equal to number of digits in base 7.

1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 121, 169, 289, 343, 346, 355, 358, 362, 365, 371, 377, 381, 382, 386, 391, 393, 394, 395, 398, 403, 407, 411, 413, 415, 417, 422, 427, 437, 445, 446, 447, 451, 453, 454, 458, 466, 469, 471, 473, 478, 481

Offset: 1

Author

M. F. Hasler, Nov 28 2007

Keywords

• base
• nonn

Comments

Since 7 is a prime, any power 7^k has k+1 divisors { 7^i ; i=0..k } and the same number of digits in base 7; thus the sequence A000420(k)=7^k is a subsequence of this one.

Examples

			a(1) = 1 since 1 has 1 divisor and 1 digit (in base 7 as in any other base).
All other numbers have at least 2 divisors so there are no other members of the sequence below a(2) = 7 = 10_7 having 2 divisors { 1, 7 } and 2 digits in base 7.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1250
• Abel Jansma, E_8 Symmetry Structures in the Ising model, Master's thesis, University of Amsterdam, 2018.

Crossrefs

Cf. A135772-A135779, A095862.

Programs

Mathematica

Select[Range[500],DivisorSigma[0,#]==IntegerLength[#,7]&] (* Harvey P. Dale, Feb 14 2015 *)

PARI

for(d=1,4,for(n=7^(d-1),7^d-1,d==numdiv(n)&print1(n", ")))