A013932 -id:A013932 - cp's OEIS frontend

A013930 Sum of first a(n) squarefrees is squarefree.

1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 20, 23, 25, 26, 27, 29, 32, 34, 37, 40, 41, 42, 43, 44, 46, 47, 49, 50, 51, 53, 54, 56, 58, 60, 61, 63, 64, 65, 69, 70, 71, 74, 76, 77, 79, 80, 81, 82, 83, 84, 86, 88, 89, 90, 92, 94, 95, 96, 98, 100, 102, 103, 104, 106, 107, 108, 110, 111

Offset: 1

Henri Lifchitz

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A005117, A013931, A013932.

Position[Accumulate[Select[Range[200], SquareFreeQ]], ?SquareFreeQ, Heads -> False] // Flatten (* _Amiram Eldar, Mar 07 2021 *)

More terms from David W. Wilson

A013931 a(n) is squarefree and sum of all squarefrees <= a(n) is squarefree.

Original entry on oeis.org

1, 2, 3, 5, 6, 10, 13, 15, 19, 22, 26, 30, 31, 35, 38, 39, 41, 43, 51, 55, 59, 65, 66, 67, 69, 70, 73, 74, 78, 79, 82, 85, 86, 89, 93, 95, 97, 102, 103, 105, 110, 111, 113, 118, 122, 123, 129, 130, 131, 133, 134, 137, 139, 142, 143, 145, 149, 154, 155, 157, 159, 163, 166, 167

Offset: 1

Henri Lifchitz

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Cf. A005117, A013930, A013932.

Module[{nn=200,sf},sf=Select[Range[nn],SquareFreeQ];Transpose[ Select[ Thread[ {sf, Accumulate[sf]}],SquareFreeQ[Last[#]]&]][[1]]] (* Harvey P. Dale, Feb 09 2013 *)

a(n) = A005117(A013930(n)). - Amiram Eldar, Mar 07 2021

More terms from David W. Wilson

A364797 Prime powers that are equal to the sum of the first k prime powers (not including 1) for some k.

Original entry on oeis.org

2, 5, 9, 29, 49, 137, 281, 359, 449, 1579, 2029, 2281, 2677, 5519, 12527, 13229, 15451, 17047, 22409, 24389, 25931, 29191, 32687, 42937, 45757, 53239, 56443, 59743, 70201, 81677, 90863, 95087, 101627, 113111, 169343, 200407, 206911, 256049, 302977, 330133, 338707, 356263

Offset: 1

Ilya Gutkovskiy, Aug 08 2023

nonn

			49 is a term because 49 is a prime power and 49 = 2 + 3 + 4 + 5 + 7 + 8 + 9 + 11.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A013918, A013921, A013932, A246655, A364796.

Select[Accumulate[Select[Range[2250], PrimePowerQ]], PrimePowerQ]

list(lim) = {my(s = 0); for(p = 1, lim, if(isprimepower(p), s += p; if(isprimepower(s), print1(s, ", "))));} \\ Amiram Eldar, Jun 20 2025

A020643 a(n)-th squarefree is sum of first k squarefrees for some k.

Original entry on oeis.org

1, 3, 5, 8, 12, 22, 36, 55, 77, 102, 133, 169, 187, 248, 296, 320, 343, 395, 483, 547, 652, 768, 809, 851, 893, 935, 1023, 1065, 1158, 1206, 1256, 1359, 1412, 1522, 1631, 1746, 1805, 1932, 1992, 2057, 2316, 2385, 2454, 2665, 2812, 2887, 3043, 3119, 3199, 3279

Offset: 1

N. J. A. Sloane, Renaud Lifchitz (100637.64(AT)CompuServe.COM), and David W. Wilson

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A005117, A013930, A013931, A013932.

With[{s = Select[Range[6000], SquareFreeQ]}, Position[s, #] & /@ Select[Accumulate[s], # <= s[[-1]] && SquareFreeQ[#] &] // Flatten] (* Amiram Eldar, Aug 19 2025 *)

A005117(a(n)) = A013932(n). - Amiram Eldar, Aug 19 2025

A364947 Prime powers that are equal to the sum of the first k prime powers (including 1) for some k.

Original entry on oeis.org

1, 3, 79, 163, 499, 947, 1279, 5297, 6689, 9629, 10853, 17467, 21001, 23887, 25411, 29761, 32089, 33289, 47947, 49429, 55633, 80687, 84697, 96157, 116719, 119159, 126641, 131783, 136991, 153371, 156227, 167861, 182969, 215249, 243161, 257921, 280897, 288853

Offset: 1

Ilya Gutkovskiy, Aug 14 2023

nonn

			79 is a term because 79 is a prime power and 79 = 1 + 2 + 3 + 4 + 5 + 7 + 8 + 9 + 11 + 13 + 16 = 1 + 2 + 3 + 2^2 + 5 + 7 + 2^3 + 3^2 + 11 + 13 + 2^4.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A000961 and A024918.

Cf. A013918, A013921, A013932, A364797

Select[Accumulate[Select[Range[2000], # == 1 || PrimePowerQ[#] &]], # == 1 || PrimePowerQ[#] &]

isp(n) = n == 1 || isprimepower(n);
list(lim) = {my(s = 0); for(p = 1, lim, if(isp(p), s += p; if(isp(s), print1(s, ", "))));} \\ Amiram Eldar, Jun 20 2025

A364948 Perfect powers that are equal to the sum of the first k perfect powers > 1 for some k.

Original entry on oeis.org

4, 121, 2548735225

Offset: 1

Ilya Gutkovskiy, Aug 14 2023

			121 is a term because 121 = 11^2 = 4 + 8 + 9 + 16 + 25 + 27 + 32 = 2^2 + 2^3 + 3^2 + 2^4 + 5^2 + 3^3 + 2^5.

Cf. A001597, A013918, A013921, A013932.

Select[Accumulate[Select[Range[3723875], GCD @@ FactorInteger[#][[All, 2]] > 1 &]], GCD @@ FactorInteger[#][[All, 2]] > 1 &]

cp's OEIS Frontend

A013930 Sum of first a(n) squarefrees is squarefree.

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A013931 a(n) is squarefree and sum of all squarefrees <= a(n) is squarefree.

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A364797 Prime powers that are equal to the sum of the first k prime powers (not including 1) for some k.

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A020643 a(n)-th squarefree is sum of first k squarefrees for some k.

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A364947 Prime powers that are equal to the sum of the first k prime powers (including 1) for some k.

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Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A364948 Perfect powers that are equal to the sum of the first k perfect powers > 1 for some k.

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Author

Keywords

Examples

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Programs

Mathematica