A066527 -id:A066527 - cp's OEIS frontend

A154588 Numbers that can be expressed as the sum of the first j integer numbers or the first k nonprime numbers, with j and k >=1.

1, 28, 435, 10296, 415416, 1062153, 3703281, 426626655, 782002378, 102886232631, 1636197988776, 2749764593278, 61972139524851, 813577626225078, 1604393353172781, 3603538956517305, 44000970048906445, 83556903098276790, 208955344344897381

Offset: 1

Paolo P. Lava & Giorgio Balzarotti, Jan 16 2009, Jan 19 2009

nonn

The indices (j,k) where A000217(j) = A051349(k) are (1,1), (7,5), (29,23), (143,123), (911,823), (1457,1327), (2721,2501), (29210,27488), (39547,37295) , (453621,433381) , (1808976,1737137) , (2345107,2253859) , (11133026,10746793), (40338012,39053670), (56646153,54880858) , (84894510,82314170) , (296651209,288273745), (408795555,397457085), (646460121,628975505). - Donovan Johnson, Sep 11 2009

			28 = A000217(7) = A051349(5).
435 = A000217(19) = A051349(23).
10296 = A000217(143) = A051349(123).

Cf. A007504, A051349, A066527, A133784, A154587.

Module[{nn=10^7,np},np=Select[Range[nn],!PrimeQ[#]&];Intersection[Accumulate[Range[ nn]],Accumulate[ np]]] (* The program generates the first 12 terms of the sequence. *) (* Harvey P. Dale, Feb 08 2024 *)

(A000217 INTERSECT A051349) MINUS {0}. - R. J. Mathar, Jan 21 2009

10256 replaced with 10296 and two more terms added by R. J. Mathar, Jan 21 2009

Extended beyond a(9) by Donovan Johnson, Sep 11 2009

A365019 Triangular numbers that for some k >= 0 are also the sum of the first k perfect powers.

Original entry on oeis.org

0, 1, 159284476

Offset: 1

Ilya Gutkovskiy, Aug 16 2023

			159284476 is a term because 159284476 = 1 + 2 + 3 + 4 + ... + 17848 = 1 + 4 + 8 + 9 + ... + 574564 = 1^2 + 2^2 + 2^3 + 3^2 + ... + 758^2.

Cf. A000217, A001597, A066527, A076408, A298270.

Join[{0}, Select[Accumulate[Select[Range[574564], # == 1 || GCD @@ FactorInteger[#][[All, 2]] > 1 &]], IntegerQ[Sqrt[8 # + 1]] &]]

cp's OEIS Frontend

A154588 Numbers that can be expressed as the sum of the first j integer numbers or the first k nonprime numbers, with j and k >=1.

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