login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A152573 The smallest superharmonic number with index n. 0
6, 30, 102, 186, 1146, 762, 8022, 5334, 35526, 23622, 145542, 49146, 540606, 344022, 2309862, 786426, 4718586, 3145722, 33030102, 22020054, 146276166, 97517382, 599260422, 399506694 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is the smallest number s such that sigma(s) divides s^n*tau(s). In short: a(n) is the smallest supersymmetric number with index n.

LINKS

Table of n, a(n) for n=1..24.

Graeme L. Cohen, Superharmonic numbers, Math. Comp. 78 (2009), 421-429.

FORMULA

a(n)= min s: A000203(s) | s^n*A000005(s).

EXAMPLE

For n=1, a(1)=6 because sigma(6)=12 divides 6^1*tau(6)=6*4=24.

PROG

(PARI) isharmonic(val, index) = ((val^index*numdiv(val) % sigma(val)) == 0)

a(n) = {val = 2; ok = 0; until (ok, if (isharmonic(val, n), if (n == 1, ok = 1, indi = 1; while (! isharmonic(val, indi), indi++); if (indi == n, ok = 1); ); ); if (! ok, val++); ); return (val); } \\ Michel Marcus, Jul 24 2013

CROSSREFS

Cf. A001599.

Sequence in context: A101855 A101375 A074007 * A258723 A225382 A245804

Adjacent sequences:  A152570 A152571 A152572 * A152574 A152575 A152576

KEYWORD

nonn

AUTHOR

R. J. Mathar, Dec 08 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 28 14:47 EDT 2020. Contains 334684 sequences. (Running on oeis4.)