A035527 Harmonic seed numbers.

1, 6, 28, 270, 496, 672, 1638, 6200, 8128, 18620, 30240, 32760, 173600, 1089270, 2229500, 2457000, 4713984, 6051500, 8506400, 17428320, 23088800, 29410290, 33550336, 45532800, 52141320, 81695250, 115048440, 142990848, 255428096

Offset: 1

Author

Jeff Burch

Keywords

• nonn

Comments

A harmonic number is a harmonic seed if it does not have a proper unitary divisor (a divisor d such that gcd(d,n/d)=1) which is harmonic.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..138 (terms < 10^14)
• G. L. Cohen and R. M. Sorli, Harmonic seeds, Fibonacci Quart., 36 No. 5 (1998) 386-390 MR1657575 (99j:11002)

Crossrefs

Cf. A001599 for harmonic numbers.

Programs

PARI

harm(n)=if(n<1,0,0==(sigma(n,0)*n)%sigma(n,1))
{a(n)=local(t);if(n<0,0,n=a(n-1); until(if(t=1,if(harm(n), fordiv(n,d, t*=((d==n)||(d==1)||(gcd(d,n/d)!=1)||!harm(d)));t,0)),n++);n)}

Extensions

Offset corrected by Donovan Johnson, Aug 21 2012