

A135777


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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^(d1), 7^d1, d==numdiv(n)&print1(n", ")))


CROSSREFS

Cf. A135772A135779, 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



