login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A168003 Orderly numbers (mod tau(n)+3). 2
7, 37, 67, 97, 127, 157, 255, 277, 307, 337, 367, 397, 457, 487, 547, 577, 607, 727, 757, 787, 877, 907, 915, 937, 967, 997, 1087, 1117, 1237, 1245, 1297, 1327, 1447, 1567, 1597, 1627, 1657, 1747, 1777, 1867, 1905, 1987, 2017, 2125, 2137, 2235, 2287, 2347 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A167408 for information about orderly numbers. It appears that when n is in this sequence, then tau(n)+3 must be a prime p such that 2 is not a square mod p (A003629). For each one of those primes, it is possible to find all forms of n that are orderly. In particular, the form n=p^k*q is in this sequence when 2k+5 is in A001122. In that case, we have the congruences p=2+tau(n)/2 and q=1+tau(n)/2 (mod tau(n)+3). When tau(n) is a multiple of 8, then another pair of congruences is p=1+tau(n)/2 and q=2+tau(n)/2 (mod tau(n)+3).

LINKS

Table of n, a(n) for n=1..48.

FORMULA

An exhaustive search over forms of n having a prime value of tau(n)+3 finds that terms of this sequence satisfy the following congruences for tau(n)+3 < 60.

. p with prime p = 2 mod 5

. p^3*q with primes {p,q} == {5,6} mod 11

. p^3*q with primes {p,q} == {6,5} mod 11

. p*q*r with primes {p,q,r} == {3,5,6} mod 11

. p^4*q with primes {p,q} == {7,6} mod 13

. p^7*q with primes {p,q} == {9,10} mod 19

. p^7*q with primes {p,q} == {10,9} mod 19

. p^3*q*r with primes {p,q,r} == {5,9,10} mod 19

. p^3*q*r with primes {p,q,r} == {9,6,10} mod 19

. p^3*q*r with primes {p,q,r} == {10,6,9} mod 19

. p*q*r*s with primes {p,q,r,s} == {5,6,9,10} mod 19

. p^12*q with primes {p,q} == {15,14} mod 29

. p^16*q with primes {p,q} == {19,18} mod 37

. p^4*q*r*s with primes {p,q,r,s} == {14,13,15,22} mod 43

. p^4*q*r*s with primes {p,q,r,s} == {31,22,24,38} mod 43

. p^24*q with primes {p,q} == {27,26} mod 53

. p^4*q^4*r with primes {p,q,r} == {5,27,26} mod 53

. p^27*q with primes {p,q} == {29,30} mod 59

. p^27*q with primes {p,q} == {30,29} mod 59

. p^13*q*r with primes {p,q,r} == {15,29,30} mod 59

. p^13*q*r with primes {p,q,r} == {29,30,36} mod 59

. p^13*q*r with primes {p,q,r} == {30,29,36} mod 59

. p^6*q^3*r with primes {p,q,r} == {29,53,30} mod 59

. p^6*q^3*r with primes {p,q,r} == {30,6,29} mod 59

. p^6*q^3*r with primes {p,q,r} == {48,29,30} mod 59

. p^6*q^3*r with primes {p,q,r} == {48,30,29} mod 59

. p^6*q*r*s with primes {p,q,r,s} == {7,28,30,45} mod 59

. p^6*q*r*s with primes {p,q,r,s} == {15,29,30,36} mod 59

. p^6*q*r*s with primes {p,q,r,s} == {29,30,36,53} mod 59

. p^6*q*r*s with primes {p,q,r,s} == {30,6,29,36} mod 59

. p^6*q*r*s with primes {p,q,r,s} == {48,15,29,30} mod 59

Andrew Weimholt found some of these forms.

CROSSREFS

Sequence in context: A123084 A123085 A128471 * A132231 A289353 A221982

Adjacent sequences: A168000 A168001 A168002 * A168004 A168005 A168006

KEYWORD

nonn

AUTHOR

T. D. Noe, Nov 16 2009

EXTENSIONS

Comment corrected and congruences mod 43 added by T. D. Noe, Dec 02 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 11:43 EST 2022. Contains 358693 sequences. (Running on oeis4.)