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

1,2

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.

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.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A135772-A135779, A095862.

Sequence in context: A161850 A007775 A070884 * A090459 A090417 A020631

Adjacent sequences: A135774 A135775 A135776 * A135778 A135779 A135780

Keyword

base,nonn

Author

M. F. Hasler, Nov 28 2007

Status

approved