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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^(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

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Last modified May 8 19:28 EDT 2021. Contains 343666 sequences. (Running on oeis4.)