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A238403 Number of ways a number can be decomposed as a sum of the form pq + qr + rp where p < q < r are distinct primes. 2
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,71

COMMENTS

The average value of a(n) is >> sqrt(n)/log^3 n. - Charles R Greathouse IV, Feb 26 2014

LINKS

Jean-François Alcover, Table of n, a(n) for n = 1..1000

EXAMPLE

71 = 3*5 + 5*7 + 7*3 = 2*3 + 3*13 + 13*2, therefore a(71) = 2.

MATHEMATICA

r[n_, p_] := Reduce[p < q < r && p*q+q*r+r*p == n, {q, r}, Primes]; a[n_] := (For[cnt = 0; p = 2, p <= Ceiling[(n-6)/5], p = NextPrime[p], rnp = r[n, p]; If[rnp =!= False, Which[rnp[[0]] === And, Print["n = ", n, " ", {p, q, r} /. ToRules[rnp]]; cnt++, rnp[[0]] === Or, Print["n = ", n, " ", {p, q, r} /. {ToRules[rnp]}]; cnt += Length[rnp], True, Print["error: n = ", n, " ", rnp]]]]; cnt); Table[a[n], {n, 1, 100}]

PROG

(PARI) list(n)=my(v=vector(n)); forprime(r=5, (n-6)\5, forprime(q=3, min((n-2*r)\(r+2), r-2), my(S=q+r, P=q*r); forprime(p=2, min((n-P)\S, q-1), v[p*S+P]++))); v \\ Charles R Greathouse IV, Feb 26 2014

(PARI) a(n)=my(s); forprime(r=(sqrtint(3*n-3)+5)\3, (n-6)\5, forprime(q= sqrtint(r^2+n)-r+1, min((n-2*r)\(r+2), r-2), if((n-q*r)%(q+r)==0 && isprime((n-q*r)/(q+r)), s++))); s \\ Charles R Greathouse IV, Feb 26 2014

CROSSREFS

Cf. A238403, A087053, A087054.

Sequence in context: A228594 A281669 A014083 * A112315 A295663 A005926

Adjacent sequences:  A238400 A238401 A238402 * A238404 A238405 A238406

KEYWORD

nonn

AUTHOR

Jean-François Alcover, Feb 26 2014

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)