A056602 - OEIS

A056602

Numbers A such that there is an equation of the form (A = Product of m + 1 primes) = (B = Product of m primes) + (C = Product of m primes), where A*B*C is a primorial number (A002110).

10, 231, 2958, 226083

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OFFSET

1,1

COMMENTS

Terms have been verified. There are no additional terms for m <= 7. - Rick L. Shepherd, Jun 16 2008

(C(3m+1,m+1)*C(2m,m))/(C(3m-2,m)*C(2m-2,m-1)) = (27m^2-1)/(m^2+1), so for a brute-force search for large m, about 27 times as many cases must be examined for m as for m-1. - Rick L. Shepherd, Jun 16 2008

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

10 = (2*5) = 3+7;

231 = (3*7*11) = (2*5)+(13*17);

2958 = (2*3*17*29) = (5*13*23)+(7*11*19);

226083 = (3*11*13*17*31) = (2*7*19*23)+(5*29*37*41).

CROSSREFS

Cf. A057035, A056600, A002110.

Sequence in context: A276019 A004702 A027952 * A349731 A239772 A239773

Adjacent sequences: A056599 A056600 A056601 * A056603 A056604 A056605

KEYWORD

more,nonn

AUTHOR

Naohiro Nomoto, Aug 21 2000

STATUS

approved