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

Author

Jonathan Vos Post, Dec 22 2007

Keywords

• nonn

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.

Examples

			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
		

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.

Crossrefs

Cf. A001358, A007592, A100959.

Programs

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

Formula

A100959 INTERSECTION A007592.

Extensions

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