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A260905 Totients of the Blum integers. 1
12, 20, 36, 44, 60, 60, 84, 108, 92, 132, 116, 132, 180, 140, 180, 156, 164, 220, 252, 204, 212, 276, 300, 252, 260, 348, 276, 396, 300, 396, 420, 324, 420, 332, 460, 356, 468, 380, 492, 540, 396, 420, 580, 444, 452, 660, 476, 612, 660, 636, 500, 700, 524 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1996.

Wikipedia, Blum Integers

Wikipedia, Euler Phi Function

FORMULA

a(n) = phi(Blum(n)) = A000010(A016105(n)), where phi(n) is Euler's totient function and Blum(n) is the n-th Blum integer.

a(n) = (A195758(n)-1)*(A195759(n)-1). - Jianing Song, Sep 16 2019

EXAMPLE

For the first Blum integer, a(1) = phi(21) = 12.

MAPLE

N:= 1000: # to get all terms <= N

Primes:= select(isprime, [seq(4*i+3, i=0.. floor(N/12 - 3/4))]):

Pairs:= select(t -> t[1]*t[2]<=N, [seq(seq([Primes[i], Primes[j]], j=i+1..nops(Primes)), i=1..nops(Primes))]):

map(t -> (t[1]-1)*(t[2]-1), sort(Pairs, (s, t) -> s[1]*s[2] < t[1]*t[2])); # Robert Israel, Nov 18 2015

MATHEMATICA

EulerPhi@ With[{lim = 820}, Select[Union[Times @@@ Subsets[Select[Prime@ Range@ PrimePi@ NextPrime[lim/3], Mod[#, 4] == 3 &], {2}]], # <= lim &]] (* Michael De Vlieger, Nov 18 2015, after Harvey P. Dale at A016105 *)

EulerPhi[Select[4Range[5, 197] + 1, PrimeNu[#] == 2 && MoebiusMu[#] == 1 && Mod[FactorInteger[#][[1, 1]], 4] != 1 &]] (* Alonso del Arte, Nov 18 2015 *)

PROG

(Perl) use ntheory ":all"; forcomposites { say euler_phi($_) if ($_ % 4) == 1 && is_square_free($_) && scalar(factor($_)) == 2 && !scalar(grep { ($_ % 4) != 3 } factor($_)); } 1000; # Dana Jacobsen, Dec 10 2015

CROSSREFS

Cf. A000010, A016105, A195758, A195759.

Sequence in context: A299028 A082296 A187766 * A211415 A209973 A282754

Adjacent sequences:  A260902 A260903 A260904 * A260906 A260907 A260908

KEYWORD

nonn,easy

AUTHOR

Connor Zapfel, Nov 17 2015

STATUS

approved

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Last modified August 1 09:08 EDT 2021. Contains 346385 sequences. (Running on oeis4.)