A221793 -id:A221793 - cp's OEIS frontend

A221792 Number of n-digit cuban primes.

1, 3, 7, 17, 36, 109, 265, 762, 2125, 5964, 17205, 49989, 145047, 424155, 1250298, 3697457, 10985390, 32768938, 98054446, 294239322, 885300000, 2669959359, 8069333311, 24435519147

Offset: 1

Vladimir Pletser, Jan 25 2013

Cf. A002407, A113478, A221793.

a(n) = A113478(n) - A113478(n-1). - Jens Kruse Andersen, Jul 14 2014

a(19)-a(24) added from A113478 by Andrew Howroyd, Jan 14 2020

A221848 Partial sums of primes equal (x+1)^5 - x^5.

Original entry on oeis.org

31, 242, 4893, 65944, 437225, 1161126, 2964127, 5825588, 10154739, 15080020, 22166471, 30110772, 44945803, 64557704, 87939735, 132059086, 186723797, 273272598, 371065129, 533543630, 723425661, 990642712, 1283752673, 1590492954, 2080592455

Offset: 1

Vladimir Pletser, Jan 26 2013

Partial sums of primes equal to the difference of two consecutive fifth powers (x+1)^5 - x^5 = 5x(x+1)(x^2+x+1)+1 (A121616). Values of x = A121617. Number of primes equal (x+1)^5 - x^5 < 10^(n) in A221846. Partial sums of number of primes of the form (x+1)^5 - x^5 have similar characteristics to similar sequences for natural primes (A007504) and cuban primes (A221793).

Vladimir Pletser, Table of n, a(n) for n = 1..1000

Accumulate[Select[#[[2]]-#[[1]]&/@Partition[Range[100]^5,2,1],PrimeQ]] (* Harvey P. Dale, Mar 29 2013 *)

More terms from Harvey P. Dale, Mar 29 2013

A221979 Partial sums of primes of the form (n+1)^7 - n^7.

Original entry on oeis.org

127, 14324, 557931, 1831540, 4517357, 9734388, 26079025, 167982242, 2096276793, 10354981402, 24379848623, 47195272710, 78109546591, 169264277168, 285424955019, 468934979410, 749602296677, 1302535107108, 2819580695167, 4457920826414

Offset: 1

Vladimir Pletser, Feb 02 2013

Partial sums of primes equal to the difference of two consecutive seventh powers (x+1)^7 - x^7 = 7x(x+1)(x^2+x+1)^2+1 (A121618). Values of x = A121619 - 1. Number of primes equal (x+1)^7 - x^7 < 10^(n) in A221977. Partial sums of number of primes of the form (x+1)^7 - x^7 have similar characteristics to similar sequences for natural primes (A007504), cuban primes (A221793) and primes of the form (x+1)^5 - x^5 (A221848).

Vladimir Pletser, Table of n, a(n) for n = 1..1000

Accumulate[Select[Differences[Range[80]^7],PrimeQ]] (* Harvey P. Dale, Jul 09 2024 *)

A221985 Partial sums of primes of the form (n+1)^11 - n^11.

Original entry on oeis.org

313968931, 6926576780, 75545517171, 2332950292798, 26362646685307289, 157261278401555730, 11893629184686938707, 40838913299508512438, 270600054840430038249, 203248659302772610786786, 431646786892325713723157, 907860322879288498305774, 2535699587078276763578623

Offset: 1

Vladimir Pletser, Feb 02 2013

Partial sums of primes equal to the difference of two consecutive eleventh powers (x+1)^11 - x^11 = 11x(x+1)(x^2+x+1)[ x(x+1)(x^2+x+1)(x^2+x+3)+1] +1 (A189055). Values of x = A211184. Number of primes equal (x+1)^11 - x^11 < 10^(n) in A221983. Partial sums of number of primes of the form (x+1)^11 - x^11 have similar characteristics to similar sequences for natural primes (A007504), cuban primes (A221793) and primes of the form (x+1)^p - x^p for p = 5 (A221848) and p = 7 (A221979).

Vladimir Pletser, Table of n, a(n) for n = 1..1000

Accumulate[Select[Differences[Range[300]^11],PrimeQ]] (* Harvey P. Dale, Mar 24 2023 *)

A268861 Cubefree numbers n such that n + 1 is a perfect cube.

Original entry on oeis.org

7, 26, 63, 124, 215, 342, 511, 1330, 1727, 2196, 2743, 3374, 4095, 7999, 9260, 10647, 12166, 13823, 17575, 19682, 24388, 26999, 29790, 32767, 39303, 42874, 46655, 54871, 59318, 63999, 74087, 79506, 85183, 91124, 103822, 110591, 124999, 132650, 140607, 148876

Offset: 1

K. D. Bajpai, Feb 14 2016

nonn

Intersection of A004709 and A068601. - Michel Marcus, Feb 15 2016

			a(2) = 26 = 2 * 13 that is cubefree. 26 + 1 = 27 = 3^3 (perfect cube).
a(4) = 124 = 2 * 2 * 31 that is cubefree. 124 + 1 = 125 = 5^3 (perfect cube).

K. D. Bajpai, Table of n, a(n) for n = 1..400

Cf. A004709, A068601, A121628, A221793, A268752.

cubefree:= proc(n) local t;
  max(seq(t[2],t=ifactors(n)[2])) <= 2
end proc:
select(cubefree, [seq(i^3-1,i=2..100)]); # Robert Israel, Mar 03 2016

Select[Range[150000], FreeQ[FactorInteger[#], {, k /; k > 2}] && IntegerQ[CubeRoot[# + 1]] &]
Select[Range[2,70]^3,Max[FactorInteger[#-1][[All,2]]]<3&]-1 (* Harvey P. Dale, Oct 11 2021 *)

for(n=1, 1e5, f = factor(n)[, 2]; if((#f == 0) || vecmax(f) < 3, if(ispower(n + 1, 3), print1(n, ", "))));

cp's OEIS Frontend

A221792 Number of n-digit cuban primes.

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A221848 Partial sums of primes equal (x+1)^5 - x^5.

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A221979 Partial sums of primes of the form (n+1)^7 - n^7.

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A221985 Partial sums of primes of the form (n+1)^11 - n^11.

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A268861 Cubefree numbers n such that n + 1 is a perfect cube.

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