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

1,2

Comments

A harmonic number is a harmonic seed if it does not have a proper unitary divisor (a divisor d > 1 such that gcd(d,n/d)=1), which is harmonic. - minor correction by Antti Karttunen, Sep 19 2025

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)

Prog

(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)}
(PARI)
is_A001599(n) = (1==denominator(n*numdiv(n)/sigma(n)));
is_A035527(n)  = if(!is_A001599(n), 0, fordiv(n, d, if(d>1 && d<n && 1==gcd(d, n/d) && is_A001599(d), return(0))); (1)); \\ Antti Karttunen, Sep 19 2025

Crossrefs

Subsequence of A001599 (harmonic numbers), which is a subsequence of A388268.

Cf. A000396 (at least the even terms are subsequence).

Sequence in context: A281003 A049603 A333927 * A388035 A220437 A332465

Adjacent sequences: A035524 A035525 A035526 * A035528 A035529 A035530

Keyword

nonn

Author

Jeff Burch

Extensions

Offset corrected by Donovan Johnson, Aug 21 2012

Status

approved