A110080 -id:A110080 - cp's OEIS frontend

A111187 a(n) is the index of A110080 where n appears.

Original entry on oeis.org

1, 5, 2, 10, 1436, 3, 99, 23355, 21, 8, 4, 42, 161289

Offset: 1

Hans Havermann, Oct 19 2005, Nov 02 2005

nonn

a(14)>1100000

A110079 Numbers n such that sigma(n)=2n-2^d(n) where d(n) is number of positive divisors of n.

Original entry on oeis.org

5, 38, 284, 1370, 2168, 26828, 133088, 1515608, 19414448, 23521328, 25812848, 49353008, 82988756, 103575728, 537394688, 558504608, 921747488, 2651596448, 17517611968, 18249863488, 77792665408, 556915822208

Offset: 1

Farideh Firoozbakht, Aug 03 2005

If 4^m+2^m-1 is prime then n=2^(m-1)*(4^m+2^m-1) is in the sequence because 2n-2^d(n)=2^m*(4^m+2^m-1)-2^(m*2)=2^m* (4^m-1)=2^m*(2^m-1)*(2^m+1)=(2^m-1)*(4^m+2^m)=sigma(2^(m-1)) *sigma(4^m+2^m-1)=sigma(2^(m-1)*(4^m+2^m-1))=sigma(n). A110082 gives such terms of this sequence.
a(22) <= 556915822208. a(23) <= 9311639470208. a(24) <= 29297682437888. - Donovan Johnson, Jan 31 2009
a(23) > 6*10^12. - Giovanni Resta, Aug 14 2013

Cf. A110080-3.

Do[If[DivisorSigma[1, n] == 2n - 2^DivisorSigma[0, n], Print[n]], {n, 925000000}]

a(18)-a(21) from Donovan Johnson, Jan 31 2009

a(22) confirmed by Giovanni Resta, Aug 14 2013

A110082 Numbers of the form 2^(m-1)*(4^m+2^m-1) where 4^m+2^m-1 is prime.

Original entry on oeis.org

5, 38, 284, 2168, 133088, 537394688, 140739635806208, 2361183382172302573568, 151115729703628426969088, 20282409604241966234288777068544, 45671926166590726335069952848216804538059849728

Offset: 1

Farideh Firoozbakht, Aug 03 2005

nonn

This sequence is a subsequence of A110079 namely, if n is in the sequence then sigma(n)=2n-2^d(n) where d(n) is number of positive divisors of n(see comments line of the sequence A110079). Sequence A110080 gives numbers n such that 4^n+2^n-1 is prime.

			2^1299*(4^1300+2^1300-1) is in the sequence because 4^1300+2^1300-1 is prime.

F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1

Cf. A110079, A098855.

Do[If[PrimeQ[4^m+2^m-1], Print[2^(m-1)*(4^m+2^m-1)]], {m, 52}]

A111118 a(1) = 1; skipping over integers occurring earlier in the sequence, count down c(n) (c(n) = n-th composite) from a(n) to get a(n+1). If this is <= 0, instead count up from a(n) c(n) positions (skipping already occurring integers) to get a(n+1).

Original entry on oeis.org

1, 5, 11, 2, 13, 23, 9, 26, 7, 28, 3, 31, 52, 29, 55, 25, 57, 22, 59, 19, 62, 17, 64, 15, 66, 10, 68, 6, 71, 115, 69, 117, 63, 119, 60, 121, 56, 124, 53, 126, 50, 128, 47, 131, 45, 133, 43, 135, 40, 137, 38, 140, 35, 142, 33, 144, 30, 147, 24, 149, 18, 151, 14, 153, 8, 156

Offset: 1

Leroy Quet, Oct 15 2005

nonn

If we did not skip earlier occurring integers when counting, we would instead have sequence A100298.

			The first 4 terms of the sequence can be plotted on the number line as:
1,2,*,*,5,*,*,*,*,*,11,*,*.
Now a(4) is 2. Counting c(4) = 9 down from 2 gets a negative integer. So we instead count up 9 positions, skipping the 5 and 11 as we count, to arrive at 13 (which is at the rightmost * of the number line above).

Cf. A100298, A110080, A002808.

More terms from Klaus Brockhaus, Oct 17 2005

cp's OEIS Frontend

A111187 a(n) is the index of A110080 where n appears.

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A110079 Numbers n such that sigma(n)=2n-2^d(n) where d(n) is number of positive divisors of n.

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A110082 Numbers of the form 2^(m-1)*(4^m+2^m-1) where 4^m+2^m-1 is prime.

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A111118 a(1) = 1; skipping over integers occurring earlier in the sequence, count down c(n) (c(n) = n-th composite) from a(n) to get a(n+1). If this is <= 0, instead count up from a(n) c(n) positions (skipping already occurring integers) to get a(n+1).

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