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A135775 Numbers having number of divisors equal to number of digits in base 5. 1
1, 5, 7, 11, 13, 17, 19, 23, 25, 49, 121, 125, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 177, 178, 183, 185, 187, 194, 201, 202, 203, 205, 206, 209, 213, 214, 215, 217, 218, 219, 221, 226, 235, 237, 247, 249, 253, 254, 259, 262, 265, 267 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Since 5 is a prime, any power 5^k has k+1 divisors { 5^i ; i=0..k } and the same number of digits in base 5; thus the sequence A000351(k)=5^k is a subsequence of this one. It also includes the powers of 7 up to 7^4, since (7/5)^4 < 5 < (7/5)^5.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

EXAMPLE

a(1) = 1 since 1 has 1 divisor and 1 digit (in base 5).

2,3,4 have 2 resp. 3 divisors but only 1 digit in base 5, so they are not members of the sequence.

a(2) = 5 = 10_5 has 2 divisors { 1, 5 } and 2 digits in base 5, so it is (the second term) in this sequence.

MATHEMATICA

Select[Range[300], DivisorSigma[0, #]==IntegerLength[#, 5]&] (* Harvey P. Dale, Mar 14 2013 *)

PROG

(PARI) for(d=1, 4, for(n=5^(d-1), 5^d-1, d==numdiv(n)&print1(n", ")))

CROSSREFS

Cf. A135772-A135779, A095862.

Sequence in context: A290729 A314295 A288155 * A219016 A276378 A243292

Adjacent sequences:  A135772 A135773 A135774 * A135776 A135777 A135778

KEYWORD

base,nonn

AUTHOR

M. F. Hasler, Nov 28 2007

STATUS

approved

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Last modified May 9 05:11 EDT 2021. Contains 343688 sequences. (Running on oeis4.)