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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A057949 Numbers with more than one factorization into S-primes. See A054520 and A057948 for definition. 9
441, 693, 1089, 1197, 1449, 1617, 1881, 1953, 2205, 2277, 2541, 2709, 2793, 2961, 3069, 3249, 3381, 3465, 3717, 3933, 3969, 4221, 4257, 4389, 4473, 4557, 4653, 4761, 4977, 5229, 5301, 5313, 5445, 5733, 5841, 5929, 5985, 6237, 6321, 6417, 6489, 6633 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers with k >= 4 prime factors (with multiplicity) that are congruent to 3 mod 4, no k-1 of which are equal. - Charlie Neder, Nov 03 2018
LINKS
EXAMPLE
2205 is in S = {1,5,9, ... 4i+1, ...}, 2205 = 5*9*49 = 5*21^2; 5, 9, 21 and 49 are S-primes (A057948).
PROG
(Sage)
def A057949_list(bound) :
numterms = (bound-1)//4 + 1
M = [1] * numterms
for k in range(1, numterms) :
if M[k] == 1 :
kpower = k
while kpower < numterms :
step = 4*kpower+1
for j in range(kpower, numterms, step) :
M[j] *= 4*k+1
kpower = 4*kpower*k + kpower + k
# Now M[k] contains the product of the terms p^e where p is an S-prime
# and e is maximal such that p^e divides 4*k+1
return [4*k+1 for k in range(numterms) if M[k] > 4*k+1]
# Eric M. Schmidt, Dec 11 2016
(PARI) ok(n)={if(n%4==1, my(f=factor(n)); my(s=[f[i, 2] | i<-[1..#f~], f[i, 1]%4==3]); vecsum(s)>=4 && vecmax(s)<vecsum(s)-1, 0)} \\ Andrew Howroyd, Nov 25 2018
CROSSREFS
Cf. A343826 (only 1 way), A343827 (exactly 2 ways), A343828 (exactly 3 ways).
Sequence in context: A207045 A252201 A252194 * A057950 A343827 A250808
KEYWORD
nonn
AUTHOR
Jud McCranie, Oct 14 2000
EXTENSIONS
Offset corrected by Eric M. Schmidt, Dec 11 2016
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 March 28 14:13 EDT 2024. Contains 371254 sequences. (Running on oeis4.)