login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

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

Corrected comment and added congruences mod 43 -- 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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 17 19:40 EST 2017. Contains 294834 sequences.