cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A144672 Numbers x,y,z such that UnitarySigma(x) = UnitarySigma(y) = UnitarySigma(z) = 3*(x*y*z)^(1/2)/(- x^(1/2) + 8*y^(1/2) - 5*z^(1/2)), z<=y<=x; sequence gives x.

Original entry on oeis.org

2, 20, 24, 360, 816, 1056, 12240, 15840, 29120, 181632, 337977, 2724480, 93358848, 1400382720
Offset: 1

Views

Author

Yasutoshi Kohmoto, Feb 02 2009

Keywords

Comments

a(11) is the smallest term for x!=y, y!=z, x!=z.
If x=y=z then we get multiply unitary perfect numbers such that UnitarySigma(x)=3x/2.

Examples

			Factorization of a(11) : 17*3^2*47^2.
		

Crossrefs

Cf. A034448, A144673, A144674 (these entries all differ at a(11)).

A144674 Numbers x,y,z such that UnitarySigma(x) = UnitarySigma(y) = UnitarySigma(z) = 3*(x*y*z)^(1/2)/(- x^(1/2) + 8*y^(1/2) - 5*z^(1/2)), z<=y<=x; sequence gives z.

Original entry on oeis.org

2, 20, 24, 360, 816, 1056, 12240, 15840, 29120, 181632, 287300, 2724480, 93358848, 1400382720
Offset: 1

Views

Author

Yasutoshi Kohmoto, Feb 02 2009

Keywords

Examples

			Factorization of a(11) : 17*5^2*2^2*13^2.
		

Crossrefs

A145680 a(n) = smallest number m such that UnitarySigma(m) = nm/(n-1).

Original entry on oeis.org

6, 2, 3, 4, 5, 216, 7, 8, 9, 5292000, 11, 10584000, 13, 4991499040640000, 165375, 16, 17, 235270656, 19, 101867327360000, 8107610881081625211441398582431641600000, 19235716742537891017605454376709022095843377283072000000, 23, 552063590295800832, 25
Offset: 2

Views

Author

Yasutoshi Kohmoto Mar 09 2009

Keywords

Comments

If n=p^i+1 then a(n)=p^i.
Unitary sigma = A034448 = sum of divisors d with gcd(d,m/d)=1.
Note that a(27) > 10^70. - Jack Brennen, Feb 04 2014

Examples

			UnitarySigma(216) = 2^2*3^2*7 = (7/6)*216.
		

Crossrefs

Cf. A034448.
Related sequences include A145681 (and A144672, A144673, A144674) for 3/2-URPMS, and A144949-A144951 for 5/4-URPMS. - M. F. Hasler, Jan 29 2014

Extensions

Corrected a(13) and added a(22) found by Jack Brennen. M. F. Hasler, Feb 04 2014
a(23)-a(26) from Jack Brennen, Feb 04 2014

A145681 Numbers m such that A034448(m) = 3m/2, where A034448 = unitary sigma = sum of divisors d with gcd(d,m/d)=1.

Original entry on oeis.org

2, 20, 24, 360, 816, 1056, 12240, 15840, 29120, 181632, 2724480, 9192960, 13790400, 15288000, 93358848, 199180800, 1130734080, 1400382720, 25115166720, 544161945600, 3089165506560, 11519246340096, 172788695101440, 274358081249280, 5944425093734400, 33746043993661440, 7425442423511040000, 25976914334122752000000, 48787315395486187520000, 56897897650906642513920
Offset: 1

Views

Author

Yasutoshi Kohmoto Mar 09 2009

Keywords

Comments

See also A144672, A144673 and A144674. These three and the present one all differ only by one or two terms around a(11)-a(12). More explanations would be welcome. - M. F. Hasler, Jan 29 2014

Crossrefs

Cf. A034448.

Extensions

Corrected and extended by Jack Brennen, Jan 30 2014
Showing 1-4 of 4 results.