A328860
Numbers that are 4-imperfect.
Original entry on oeis.org
993803899780063855042560, 2028353759451110328141864960, 6476620014866676143312363520
Offset: 1
- Douglas E. Iannucci, On a variation of perfect numbers, INTEGERS: Electronic Journal of Combinatorial Number Theory, 6 (2006), #A41.
- Andrew Lelechenko, 4-imperfect numbers, Apr 19 2014.
- Michel Marcus, More 4-imperfect numbers, Nov 07 2017.
- Michel Marcus, solveIMP PARI script
- Michel Marcus, List of 4-imperfect numbers (including the 2 files above), last edit Jun 2019.
- Weiyi Zhou and Long Zhu, On k-imperfect numbers, INTEGERS: Electronic Journal of Combinatorial Number Theory, 9 (2009), #A01.
A200758
Superimperfect numbers.
Original entry on oeis.org
2, 4, 8, 128, 32768, 2147483648
Offset: 1
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beta(n)=sumdiv(n,d,(-1)^bigomega(n/d)*d)
for(n=1,1e8,if(2*beta(beta(n))==n,print1(n", "))) \\ Charles R Greathouse IV, Nov 22 2011
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ak(p,e)=my(s=1); for(i=1,e, s=s*p + (-1)^i); s
beta(n)=my(f=factor(n)); prod(i=1,#f~, ak(f[i,1],f[i,2]))
is(n)=my(b=beta(n)); 2*b-2 >= n && 2*beta(b)==n \\ Charles R Greathouse IV, Dec 27 2016
A309553
Imperfect numbers of the form 2^(2^k-1)*F_1*F_2*...*F_(k-1), where F is a Fermat number.
Original entry on oeis.org
40, 10880, 715816960, 3074457344902430720
Offset: 1
For k=2, 2^3*F_1 = 8*5 = 40, so 40 is in the sequence.
- László Tóth, A survey of the alternating sum-of-divisors function, arXiv:1111.4842 [math.NT], 2011-2014, end of section 8.
- László Tóth, A survey of the alternating sum-of-divisors function, Acta Universitatis Sapientiae, Mathematica, Vol. 5, No. 1 (2013), pp. 93-107.
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