A133447 Nonsemiprime hyperperfect numbers.

325, 2133, 10693, 16513, 19521, 51301, 159841, 176661, 214273, 306181, 1433701, 1570153, 1950625, 2469601, 2924101, 5199013, 9398593, 10445221, 15407173, 23548753, 28600321, 39147301, 60110701, 62722153, 88347781, 112803841

Offset

1,1

Comments

The other 25 of the first 35 values of A007592 are all semiprimes A001358.

This sequence excludes perfect numbers (A000396), which are 1-hyperperfect numbers. - Jud McCranie, Mar 23 2025.

Links

Jud McCranie, Table of n, a(n) for n = 1..1167 (terms < 10^15). Earlier terms from Jonathan Vos Post and R. J. Mathar, and a b-file with 192 terms (to 10^12) by Donovan Johnson.

Formula

A100959 INTERSECTION A007592.

Example

a(1) = 325 = 5^2 * 13.
a(2) = 2133 = 3^3 * 79.
a(3) = 10693 = 17^2 * 37.
a(4) = 16513 = 7^2 * 337.
a(5) = 19521 = 3^4 * 341.
a(6) = 51301 = 29^2 * 61.
a(7) = 159841 = 11^2 * 1321.
a(8) = 176661 = 3^5 * 727.
a(9) = 214273 = 47^2 * 97.
a(10) = 306181 = 53^2 * 109.
a(12) = 1570153 = 13 * 269 * 449. - Jud McCranie, Mar 23 2025

Maple

a034897 := [] : fd := fopen("b034897.txt", READ) : bf := fscanf(fd, "%d %d") : while nops(bf) <> 0 do a034897 := [op(a034897), op(2, bf) ] ; bf := fscanf(fd, "%d %d") ; od: a007592 := [] : for n in a034897 do m := (n-1)/( numtheory[sigma](n)-n-1) ; if m > 1 then a007592 := [op(a007592), n] ; fi ; od: isA100959 := proc(n) if numtheory[bigomega](n) <> 2 then true ; else false ; end: end: for n in a007592 do if isA100959(n) then printf("%d, ", n) ; fi ; od: # R. J. Mathar, Jan 08 2008

Crossrefs

Cf. A001358, A007592, A100959.

Sequence in context: A183645 A299708 A031714 * A179535 A374257 A145414

Adjacent sequences: A133444 A133445 A133446 * A133448 A133449 A133450

Keyword

nonn

Author

Jonathan Vos Post, Dec 22 2007

Extensions

More terms from R. J. Mathar, Jan 08 2008

Status

approved