A273801 -id:A273801 - cp's OEIS frontend

A273800 Numbers n for which n = phi(x)*phi(y), where n = x + y and phi(x) is the Euler totient function of x.

8, 12, 16, 24, 32, 36, 48, 96, 128, 160, 192, 288, 768, 1152, 2048, 2560, 3072, 27648, 110592, 192704, 196608, 202496, 232448, 370688, 379904, 394264, 443512, 466048, 508672, 524288, 553120, 571008, 586016, 607744, 624704, 650624, 655360, 675584, 681856

Offset: 1

Paolo P. Lava, May 31 2016

nonn

			8 = 3+5 = phi(3)*phi(5) = 2*4;
12 = 3+9 = phi(3)*phi(9) = 2*6;
24 = 3+21 = phi(3)*phi(21) = 2*12 or 24 = 10+14 = phi(10)*phi(14) = 4*6.

Giovanni Resta, Table of n, a(n) for n = 1..1000

Cf. A000010, A273801.

with(numtheory): P:=proc(q) local a,b,k,n; for n from 1 to q do
for k from 1 to trunc(n/2) do if phi(k)*phi(n-k)=n then print(n); break; fi;
od; od; end: P(10^9);

is(n)=for(x=1,n\2, if(eulerphi(x)+eulerphi(n-x)==n, return(1))); 0 \\ Charles R Greathouse IV, Jun 07 2016

a(19)-a(39) from Giovanni Resta, May 31 2016

A289055 Triangle read by rows: T(n,k) = (k+1)*A028815(n) for 0 <= k <= n.

Original entry on oeis.org

2, 3, 6, 4, 8, 12, 6, 12, 18, 24, 8, 16, 24, 32, 40, 12, 24, 36, 48, 60, 72, 14, 28, 42, 56, 70, 84, 98, 18, 36, 54, 72, 90, 108, 126, 144, 20, 40, 60, 80, 100, 120, 140, 160, 180, 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330

Offset: 0

Vincenzo Librandi, Sep 02 2017

			Triangle begins:
   2;
   3,   6;
   4,   8,  12;
   6,  12,  18,  24;
   8,  16,  24,  32,  40;
  12,  24,  36,  48,  60,  72;
  14,  28,  42,  56,  70,  84,  98;
  18,  36,  54,  72,  90, 108, 126, 144;
  20,  40,  60,  80, 100, 120, 140, 160, 180;
  ...

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Cf. A289108.

Columns k: A028815 (k=0), A089241 (k=1), A247159 (k=2), A273801 (k=3).

/* As triangle (here NthPrime(0)=1) */ [[(k+1)*(NthPrime(n)+1): k in [0..n]]: n in [0.. 15]];

Join[{2}, t[n_, k_] := (k + 1) (Prime[n] + 1); Table[t[n, k], {n, 10}, {k, 0, n}] //Flatten]

def A289055(n,k): return 2 if n==0 else (k+1)*(nth_prime(n) +1)
flatten([[A289055(n,k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Aug 05 2024

a(n) = A289108(n) + 1.

cp's OEIS Frontend

A273800 Numbers n for which n = phi(x)*phi(y), where n = x + y and phi(x) is the Euler totient function of x.

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A289055 Triangle read by rows: T(n,k) = (k+1)*A028815(n) for 0 <= k <= n.

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