A290843 -id:A290843 - cp's OEIS frontend

A159463 Numbers n with property that sod(n^3) = 6^3.

3848163483, 4462569999, 4479677412, 4586158119, 4594661259, 4594665192, 4594700889, 4625720379, 4641588459, 5644008999, 5828410842, 5833034823, 5838252576, 5848025709, 6453471192, 6617331999, 6619097067, 6686657169, 7107126942, 7230291999, 7277907183

Offset: 1

Zak Seidov, Apr 12 2009

Numbers n with property that A007953(n^3) = 6^3.

			3848163483^3 = 56984998629886989599887999587, 5+6+9+8+4+9+9+8+6+2+9+8+8+6+9+8+9+5+9+9+8+8+7+9+9+9+5+8+7 = 216 = 6^3.

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Cf. A054966 Numbers that are congruent to {0, 1, 8} mod 9. A054966 Possible sums of digits of cubes. A067075 a(n) = smallest number m such that the sum of the digits of m^3 is equal to n^3. A007953 Digital sum (i.e., sum of digits) of n.

Numbers n such that sum of digits of n^3 is k^3: A107679 (k=2), A290842 (k=3), A290843 (k=4), A159462 (k=5), this sequence (k=6).

a(16)-a(21) from Seiichi Manyama, Aug 12 2017

A290842 Numbers k such that the sum of digits of k^3 is 3^3 = 27.

Original entry on oeis.org

27, 33, 36, 39, 42, 54, 57, 69, 72, 75, 78, 84, 87, 93, 105, 108, 111, 114, 135, 138, 147, 162, 165, 168, 174, 177, 219, 222, 225, 228, 231, 234, 258, 267, 270, 273, 276, 285, 291, 294, 312, 318, 321, 330, 342, 345, 348, 351, 360, 369, 381, 384, 390, 405, 417

Offset: 1

Seiichi Manyama, Aug 12 2017

It is obvious that if k is in this sequence, then so is 10*k. Additionally, this sequence contains other infinite subsequences. For example, 10^(2*k) + 10^k + 1 is in this sequence for all k > 0. - Altug Alkan, Aug 12 2017

			27^3 = 19683, 1 + 9 + 6 + 8 + 3 = 27 = 3^3.

Seiichi Manyama, Table of n, a(n) for n = 1..500

Numbers k such that sum of digits of k^3 is m^3: A107679 (m=2), this sequence (m=3), A290843 (m=4), A159462 (m=5), A159463 (m=6).

Cf. A067075.

isok(n) = sumdigits(n^3) == 27; \\ Altug Alkan, Aug 12 2017

A290944 Primes p such that sum of digits of p^3 is a perfect square.

Original entry on oeis.org

3, 1753, 1999, 2389, 2713, 3301, 3361, 3529, 3583, 3607, 3631, 3643, 3697, 3889, 3907, 4093, 4099, 4129, 4153, 4159, 4243, 4423, 4591, 4639, 4813, 5167, 5449, 5503, 5527, 5563, 5683, 5689, 5827, 6199, 6211, 6427, 6529, 6553, 6691, 6709, 6883, 6949, 6961, 6997

Offset: 1

K. D. Bajpai, Aug 14 2017

All the terms in this sequence, except a(1), are congruent to 1 mod 3.

After a(1), all the terms are congruent to {1, 4, 7} mod 9.

			a(1) = 3 is prime: 3^3 = 27; 2 + 7 = 9 = 3^2.
a(2) = 1753 is prime: 1753^3 = 5386984777; 5 + 3 + 8 + 6 + 9 + 8 + 4 + 7 + 7 + 7 = 64 = 8^2.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A007605, A052279, A079130, A086924, A235398, A259418, A290843.

[p: p in PrimesUpTo(1000) | IsSquare(&+Intseq(p^3))];

f:= n->add(d, d=convert(n^3, base, 10)):
select(t -> type(sqrt(f(t)), integer), [seq(ithprime(m), m=1..10^3)]);

Select[Prime[Range[2000]], IntegerQ[Sqrt[Plus @@ IntegerDigits[#^3]]] &]

forprime(p=1, 5000, if(issquare(sumdigits(p^3)), print1(p, ", ")));

is(n) = ispseudoprime(n) && issquare(sumdigits(n^3)) \\ Felix Fröhlich, Aug 14 2017

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A159463 Numbers n with property that sod(n^3) = 6^3.

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A290842 Numbers k such that the sum of digits of k^3 is 3^3 = 27.

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A290944 Primes p such that sum of digits of p^3 is a perfect square.

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