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A004614 Numbers that are divisible only by primes congruent to 3 mod 4. 16
1, 3, 7, 9, 11, 19, 21, 23, 27, 31, 33, 43, 47, 49, 57, 59, 63, 67, 69, 71, 77, 79, 81, 83, 93, 99, 103, 107, 121, 127, 129, 131, 133, 139, 141, 147, 151, 161, 163, 167, 171, 177, 179, 189, 191, 199, 201, 207, 209, 211, 213, 217, 223, 227, 231, 237, 239, 243, 249, 251 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers whose factorization as Gaussian integers is the same as their factorization as integers. - Franklin T. Adams-Watters, Oct 14 2005

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

FORMULA

Product(A079261(A027748(a(n),k)): k=1..A001221(a(n))) = 1. - Reinhard Zumkeller, Jan 07 2013

MATHEMATICA

ok[1] = True; ok[n_] := And @@ (Mod[#, 4] == 3 &) /@ FactorInteger[n][[All, 1]]; Select[Range[251], ok] (* Jean-Fran├žois Alcover, May 05 2011 *)

PROG

(PARI) for(n=1, 1000, if(sumdiv(n, d, isprime(d)*if((d-3)%4, 1, 0))==0, print1(n, ", ")))

(PARI) forstep(n=1, 999, 2, for(j=1, #t=factor(n)[, 1], t[j]%4==1 && next(2)); print1(n", ")) \\ M. F. Hasler, Feb 26 2008

(PARI) list(lim)=my(v=List([1]), cur, idx, newIdx); forprime(p=3, lim, if(p%4>1, listput(v, p))); for(i=2, #v, cur=v[i]; idx=1; while(v[idx]*cur <= lim, my(newidx=#v+1, t); for(j=idx, #v, t=cur*v[j]; if(t<=lim, listput(v, t))); idx=newidx)); Set(v) \\ Charles R Greathouse IV, Feb 06 2018

(MAGMA) [n: n in [1..300] | forall{d: d in PrimeDivisors(n) | d mod 4 eq 3}]; // Vincenzo Librandi, Aug 21 2012

(Haskell)

a004614 n = a004614_list !! (n-1)

a004614_list = filter (all (== 1) . map a079261 . a027748_row) [1..]

-- Reinhard Zumkeller, Jan 07 2013

CROSSREFS

Cf. A004613.

Sequence in context: A156770 A088630 A129747 * A112398 A197504 A167800

Adjacent sequences:  A004611 A004612 A004613 * A004615 A004616 A004617

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)