A164977 -id:A164977 - cp's OEIS frontend

A035470 Number of ways to break {1,2,3,...,n} into sets with equal sums.

1, 1, 2, 2, 2, 2, 6, 12, 11, 2, 80, 166, 2, 665, 2918, 3309, 9296, 23730, 31875, 301030, 422897, 2, 13716867, 71504980, 100664385, 54148591, 880696662, 498017759, 27450476787, 111911522819, 179459955554, 2144502175214, 59115423983, 45837019664552, 375743493787258, 816118711787493, 2, 9492169507922

Offset: 1

Erich Friedman

nonn

a(n) = 2 <=> |{d|n*(n+1)/2 : d>=n}| = 2. - Alois P. Heinz, Sep 03 2009

			a(7) = 6 since we have 1234567, 16/25/34/7, 167/2345, 257/1346, 347/1256, 356/1247.
From _Gus Wiseman_, Jul 13 2019: (Start)
The a(6) = 2 through a(9) = 11 set partitions with equal block-sums:
  {123456}      {1234567}        {12345678}        {123456789}
  {16}{25}{34}  {1247}{356}      {12348}{567}      {12345}{69}{78}
                {1256}{347}      {12357}{468}      {1239}{456}{78}
                {1346}{257}      {12456}{378}      {1248}{357}{69}
                {167}{2345}      {1278}{3456}      {1257}{348}{69}
                {16}{25}{34}{7}  {1368}{2457}      {1347}{258}{69}
                                 {1458}{2367}      {1356}{249}{78}
                                 {1467}{2358}      {159}{2346}{78}
                                 {1236}{48}{57}    {159}{267}{348}
                                 {138}{246}{57}    {168}{249}{357}
                                 {156}{237}{48}    {18}{27}{36}{45}{9}
                                 {18}{27}{36}{45}
(End)

Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.

Cf. A164977, A164978. - Alois P. Heinz, Sep 03 2009
Row sums of A275714.
Row sums of A320438.
Cf. A000110, A007837, A038041, A112956, A275780, A275781, A321455, A326512, A326513, A326518, A326534.

with(numtheory): b:= proc() option remember; local i, j, t; `if`(args[1]=0, `if`(nargs=2, 1, b(args[t] $t=2..nargs)), add(`if`(args[j] -args[nargs] <0, 0, b(sort([seq(args[i] -`if`(i=j, args[nargs], 0), i=1..nargs-1)])[], args[nargs]-1)), j=1..nargs-1)) end: a:= proc(n) local i, m, x; m:= n*(n+1)/2; 1+ add(b(i$(m/i), n)/(m/i)!, i=[select(x-> x>=n, divisors(m) minus {m})[]]) end: seq(a(n), n=1..25);  # Alois P. Heinz, Sep 03 2009

b[args_List] := b[args] = If[args[[1]] == 0, If[Length[args] == 2, 1, b[Rest[args]]], Sum[If[args[[j]] - args[[-1]] < 0, 0, b[Sort[Join[Table[ args[[i]] - If[i == j, args[[-1]], 0], {i, 1, Length[args]-1}]]], {args[[-1]]-1}]], {j, 1, Length[args]-1}]]; b[a1_List, a2_List] := b[Join[a1, a2]];
a[n_] := a[n] = With[{m = n*(n+1)/2}, 1+Sum[b[Append[Array[i&, m/i], n]] / (m/i)!, {i, Select[Divisors[m] ~Complement~ {m}, # >= n &]}]];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 25}] (* Jean-François Alcover, Mar 22 2017, after Alois P. Heinz *)
sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
Table[Length[Select[sps[Range[n]],SameQ@@Total/@#&]],{n,0,10}] (* Gus Wiseman, Jul 13 2019 *)

More terms from John W. Layman, Mar 18 2002
a(19)-a(33) from Alois P. Heinz, Sep 03 2009
a(34) from Alois P. Heinz, May 24 2015
a(35)-a(38) from Max Alekseyev, Feb 15 2024

A068443 Triangular numbers which are the product of two primes.

Original entry on oeis.org

6, 10, 15, 21, 55, 91, 253, 703, 1081, 1711, 1891, 2701, 3403, 5671, 12403, 13861, 15931, 18721, 25651, 34453, 38503, 49141, 60031, 64261, 73153, 79003, 88831, 104653, 108811, 114481, 126253, 146611, 158203, 171991, 188191, 218791, 226801, 258121, 269011

Offset: 1

Stephan Wagler (stephanwagler(AT)aol.com), Mar 09 2002

These triangular numbers are equal to p * (2p +- 1).
All terms belong to A006987. For n>2 all terms are odd and belong to A095147. - Alexander Adamchuk, Oct 31 2006
A156592 is a subsequence. - Reinhard Zumkeller, Feb 10 2009
Triangular numbers with exactly 4 divisors. - Jon E. Schoenfield, Sep 05 2018

			Triangular numbers begin 0, 1, 3, 6, 10, ...; 6=2*3, and 2 and 3 are two distinct primes; 10=2*5, and 2 and 5 are two distinct primes, etc. - _Vladimir Joseph Stephan Orlovsky_, Feb 27 2009
a(11) = 1891 and 1891 = 31 * 61.

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Cf. A000217, A005382, A005384, A006987, A095147, A001358, A005385, A006881, A007304, A066179, A111206, A157342, A157344-A157347, A157352-A157357, A164977.

Cf. A075875.

q:= n-> is(numtheory[bigomega](n)=2):
select(q, [i*(i+1)/2$i=0..1000])[];  # Alois P. Heinz, Mar 27 2024

Select[ Table[ n(n + 1)/2, {n, 1000}], Apply[Plus, Transpose[ FactorInteger[ # ]] [[2]]] == 2 &]
Select[Accumulate[Range[1000]],PrimeOmega[#]==2&] (* Harvey P. Dale, Apr 03 2016 *)

list(lim)=my(v=List());forprime(p=2,(sqrtint(lim\1*8+1)+1)\4, if(isprime(2*p-1),listput(v,2*p^2-p)); if(isprime(2*p+1), listput(v,2*p^2+p))); Vec(v) \\ Charles R Greathouse IV, Jun 13 2013

A010054(a(n))*A064911(a(n)) = 1. - Reinhard Zumkeller, Dec 03 2009

a(n) = A000217(A164977(n)). - Zak Seidov, Feb 16 2015

Edited by Robert G. Wilson v, Jul 08 2002

Definition corrected by Zak Seidov, Mar 09 2008

A069904 Number of prime factors of n-th triangular number (with multiplicity).

Original entry on oeis.org

0, 1, 2, 2, 2, 2, 3, 4, 3, 2, 3, 3, 2, 3, 5, 4, 3, 3, 3, 4, 3, 2, 4, 5, 3, 4, 5, 3, 3, 3, 5, 6, 3, 3, 5, 4, 2, 3, 5, 4, 3, 3, 3, 5, 4, 2, 5, 6, 4, 4, 4, 3, 4, 5, 5, 5, 3, 2, 4, 4, 2, 4, 8, 7, 4, 3, 3, 4, 4, 3, 5, 5, 2, 4, 5, 4, 4, 3, 5, 8, 5, 2, 4, 5, 3, 3, 5, 4, 4, 5

Offset: 1

Reinhard Zumkeller, Apr 10 2002

nonn

			A000217(8) = 8*(8+1)/2 = 36 = 2*2*3*3, therefore a(8) = 4.

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A069901, A069902, A069903, A092405, A101745, A108815, A114435, A114436, A114437, A164977, A240527, A240528, A240529, A278253.

Array[Plus@@Last/@FactorInteger[ #*(#+1)/2]&,33] (* Vladimir Joseph Stephan Orlovsky, Feb 28 2010 *)

A069904(n) = bigomega((n*(n+1))/2); \\ Antti Karttunen, Oct 07 2017

a(n) = A001222(A000217(n)).
From Antti Karttunen, Oct 07 2017: (Start)
a(n) = (A001222(n)+A001222(n+1))-1.
a(n) = A001222(A278253(n)). (End)
From Alois P. Heinz, Aug 05 2019: (Start)
a(n) = 2 <=> n in { A164977 }.
a(n) = 3 <=> n in { A108815 }.
a(n) = 4 <=> n in { A114435 }.
a(n) = 5 <=> n in { A114436 }.
a(n) = 6 <=> n in { A114437 }.
a(n) = 7 <=> n in { A240527 }.
a(n) = 8 <=> n in { A240528 }.
a(n) = 9 <=> n in { A240529 }.
a(n) = 10 <=> n im { A101745 }. (End)

A350593 Numbers k such that tau(k) + tau(k+1) = 6, where tau is the number of divisors function A000005.

Original entry on oeis.org

5, 6, 7, 10, 13, 22, 37, 46, 58, 61, 73, 82, 106, 157, 166, 178, 193, 226, 262, 277, 313, 346, 358, 382, 397, 421, 457, 466, 478, 502, 541, 562, 586, 613, 661, 673, 718, 733, 757, 838, 862, 877, 886, 982, 997, 1018, 1093, 1153, 1186, 1201, 1213, 1237, 1282

Offset: 1

Jon E. Schoenfield, Jan 08 2022

nonn

Since tau(k) + tau(k+1) = 6, (tau(k), tau(k+1)) must be (1,5), (2,4), (3,3), (4,2), or (5,1); of these, (1,5) and (5,1) are impossible (tau(m) = 1 only for m=1, but then neither m+1 nor m-1 would have 5 divisors), and (3,3) is also impossible (both k and k+1 would have to be squares of primes), so (tau(k), tau(k+1)) must be either (2,4) or (4,2).
For every prime p, tau(p) = 2. For every semiprime s, tau(s) = 4, with the exception of the squares of primes; for p prime, tau(p^2) = 3, since the divisors of p^2 are 1, p, and p^2.
The only numbers that have exactly 4 divisors but are not semiprimes are the cubes of primes; for prime p, the divisors of p^3 are 1, p, p^2, and p^3.
As a result, this sequence consists of:
(1) the primes p such that (p+1)/2 is prime (A005383), with the exception of p=3 (since p+1 = 4 has 3 divisors, not 4),
(2) semiprimes of the form prime - 1 (A077065), with the exception of the semiprime 4 (since it does not have 4 divisors), and
(3) the special case k = 7, since it is the unique prime p such that p+1 has 4 divisors but is not a semiprime.
For all k > 4, tau(k) + tau(k+1) >= 6; for k = 1..4, tau(k) + tau(k+1) = 3, 4, 5, 5.

			   k  tau(k)  tau(k+1)  tau(k) + tau(k+1)
  --  ------  --------  -----------------
   1     1        2         1 + 2 = 3
   2     2        2         2 + 2 = 4
   3     2        3         2 + 3 = 5
   4     3        2         3 + 2 = 5
   5     2        4         2 + 4 = 6   so   5 = a(1)
   6     4        2         4 + 2 = 6   so   6 = a(2)
   7     2        4         2 + 4 = 6   so   7 = a(3)
   8     4        3         4 + 3 = 7
   9     3        4         3 + 4 = 7
  10     4        2         4 + 2 = 6   so  10 = a(4)
  11     2        6         2 + 6 = 8
  12     6        2         6 + 2 = 8
  13     2        4         2 + 4 = 6   so  13 = a(5)

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000

Cf. A000005, A005383, A077065, A092405, A164977.

Numbers k such that Sum_{j=0..N-1} tau(k+j) = 2*Sum_{k=1..N} tau(k): A000040 (N=1), (this sequence) (N=2), A350675 (N=3), A350686 (N=4), A350699 (N=5), A350769 (N=6), A350773 (N=7), A350854 (N=8).

Select[Range[1300], Plus @@ DivisorSigma[0, # + {0, 1}] == 6 &] (* Amiram Eldar, Jan 08 2022 *)
Position[Total/@Partition[DivisorSigma[0,Range[1300]],2,1],6]//Flatten (* Harvey P. Dale, Sep 03 2022 *)

isok(k) = numdiv(k) + numdiv(k+1) == 6; \\ Michel Marcus, Jan 08 2022

from itertools import count, islice
from sympy import divisor_count
def A350093_gen(): # generator of terms
    a, b = divisor_count(1), divisor_count(2)
    for k in count(1):
        if a + b == 6:
            yield k
        a, b = b, divisor_count(k+2)
A350093_list = list(islice(A350093_gen(),12)) # Chai Wah Wu, Jan 11 2022

{ k : tau(k) + tau(k+1) = 6 }.
UNION(A005383 \ {3}, A077065 \ {4}, {7}).
a(n) = A164977(n+1) for n>=4. - Hugo Pfoertner, Jan 08 2022

A164978 Number of divisors of n*(n+1)/2 that are >= n.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 3, 4, 3, 2, 4, 4, 2, 4, 7, 4, 3, 3, 4, 7, 4, 2, 6, 8, 3, 4, 7, 4, 4, 4, 5, 9, 4, 4, 11, 6, 2, 4, 11, 6, 4, 4, 4, 11, 6, 2, 8, 11, 4, 6, 7, 4, 4, 7, 11, 11, 4, 2, 8, 8, 2, 6, 16, 11, 7, 4, 4, 7, 8, 4, 9, 9, 2, 6, 11, 8, 8, 4, 8, 18, 5, 2, 8, 15, 4, 4, 11, 6, 6, 11, 8, 7, 4, 4, 18, 10, 3, 8

Offset: 1

Alois P. Heinz, Sep 03 2009

a(n) = 2 <=> the set S = {1..n} has only one decomposition into smaller subsets with equal element sum.

			a(6) = 2, because 6*7/2=21 with divisors {1,3,7,21}, but only 7 and 21 are >=6. S={1..6} has only one decomposition into smaller subsets with equal element sum: {1,6}, {2,5}, {3,4}.
a(7) = 3; 7*8/2=28 with divisors {1,2,4,7,14,28}, 3 of which are >=7. S={1..7} has 5 decompositions into smaller subsets with equal element sum.

Alois P. Heinz and T. D. Noe, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Cf. A164977, A035470.

with(numtheory):
a:= n-> nops(select(x-> x>=n, divisors(n*(n+1)/2))):
seq(a(n), n=1..120);

a(n) = |{d|n*(n+1)/2 : d>=n}|.

A112956 a(n) = number of ways the set {1,2,...,n} can be split into proper subsets with equal sums.

Original entry on oeis.org

0, 0, 1, 1, 1, 1, 5, 11, 10, 1, 79, 165, 1, 664, 2917, 3308, 9295, 23729, 31874, 301029, 422896, 1, 13716866, 71504979, 100664384, 54148590, 880696661, 498017758, 27450476786, 111911522818, 179459955553, 2144502175213, 59115423982, 45837019664551

Offset: 1

Floor van Lamoen, Oct 07 2005

nonn

For n=7 we have splittings 761/5432, 752/6431, 743/6521, 7421/653 and 7/61/52/43 so a(7)=5.

a(n) = 1 <=> n*(n+1)/2 is product of two primes. - Alois P. Heinz, Sep 03 2009

Cf. A035470.

Cf. A164977, A164978. - Alois P. Heinz, Sep 03 2009

with(numtheory): b:= proc() option remember; local i, j, t; `if`(args[1]=0, `if`(nargs=2, 1, b(args[t] $t=2..nargs)), add(`if`(args[j] -args[nargs] <0, 0, b(sort([seq(args[i] -`if`(i=j, args[nargs], 0), i=1..nargs-1)])[], args[nargs]-1)), j=1..nargs-1)) end: a:= proc(n) local i, m, x; m:= n*(n+1)/2; add(b(i$(m/i), n)/(m/i)!, i=[select(x-> x>=n, divisors(m) minus {m})[]]) end: seq(a(n), n=1..25);  # Alois P. Heinz, Sep 03 2009

b[args_List] := b[args] = If[args[[1]] == 0, If[Length[args] == 2, 1, b[Rest[args]]], Sum[If[args[[j]] - args[[-1]] < 0, 0, b[Sort[Join[ Table[ args[[i]] - If[i == j, args[[-1]], 0], {i, 1, Length[args] - 1}]]], {args[[-1]] - 1}]], {j, 1, Length[args] - 1}]]; b[a1_List, a2_List] := b[Join[a1, a2]];
a[n_] := a[n] = With[{m = n*(n + 1)/2}, Sum[b[Append[Array[i&, m/i], n]] / (m/i)!, {i, Select[Divisors[m] ~Complement~ {m}, # >= n&]}]];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 25}] (* Jean-François Alcover, Mar 22 2017, after Alois P. Heinz *)

a(n) = A035470(n) - 1. - Franklin T. Adams-Watters, Jun 02 2006

More terms from Franklin T. Adams-Watters, Jun 02 2006
a(19)-a(33) from Alois P. Heinz, Sep 03 2009
a(34) from Alois P. Heinz, Aug 06 2016

A240527 Indices of 7-almost prime triangular numbers.

Original entry on oeis.org

64, 95, 127, 135, 143, 144, 159, 160, 175, 191, 192, 207, 215, 216, 242, 243, 272, 279, 296, 323, 335, 350, 360, 368, 375, 404, 405, 415, 416, 431, 432, 448, 455, 459, 464, 479, 485, 504, 527, 528, 543, 544, 559, 584, 594, 615, 620, 623, 647, 656, 672, 719

Offset: 1

Vincenzo Librandi, Apr 07 2014

nonn

			a(1) = 64 because A000217(64) = 64*(64+1)/2 = 2080 = 2^5 * 5 * 13 is a 7-almost prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000217, A069904, A108815, A114435, A114436, A114437, A164977.

Flatten[Position[Accumulate[Range[800]],_?(PrimeOmega[#]==7&)]]

{ m : A069904(m) = 7 }. - Alois P. Heinz, Aug 05 2019

A240528 Indices of 8-almost prime triangular numbers.

Original entry on oeis.org

63, 80, 128, 256, 287, 288, 319, 320, 324, 383, 399, 440, 447, 480, 495, 539, 560, 567, 576, 608, 640, 648, 671, 675, 703, 720, 729, 799, 831, 863, 927, 935, 972, 975, 1000, 1007, 1055, 1056, 1071, 1079, 1080, 1104, 1119, 1120, 1160, 1175, 1183, 1184

Offset: 1

Vincenzo Librandi, Apr 07 2014

nonn

			a(1) = 63 because A000217(63) = 63*(63+1)/2 = 2016 = 2^5 * 3^2 * 7 is an 8-almost prime.

Muniru A Asiru, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Cf. A000217, A069904, A108815, A114435, A114436, A114437, A164977.

Cf. A046310 (8-almost primes).

F:=List([1..1200],n->Length(Factors(n*(n+1)/2)));; a:=Filtered([1..Length(F)],i->F[i]=8); # Muniru A Asiru, Dec 22 2018

[n: n in [2..1200] | &+[d[2]: d in Factorization((n*(n+1)))] eq 9]; // Vincenzo Librandi, Dec 22 2018

Flatten[Position[Accumulate[Range[1500]], _?(PrimeOmega[#]== 8 &)]]

{ m : A069904(m) = 8 }. - Alois P. Heinz, Aug 05 2019

A240529 Indices of 9-almost prime triangular numbers.

Original entry on oeis.org

224, 351, 624, 704, 735, 768, 783, 800, 832, 864, 895, 944, 959, 960, 999, 1151, 1152, 1224, 1279, 1343, 1344, 1375, 1440, 1520, 1539, 1824, 1855, 1935, 1943, 1944, 1952, 2000, 2144, 2159, 2176, 2187, 2295, 2367, 2430, 2432, 2464, 2495, 2496, 2499, 2511

Offset: 1

Vincenzo Librandi, Apr 07 2014

			a(1) = 224 because A000217(224) = 224*(224+1)/2 = 25200 = 2^4 * 3^2 * 5^2 * 7 is a 9-almost prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000217, A069904, A108815, A114435, A114436, A114437, A164977.

F:=List([1..2600],n->Length(Factors(n*(n+1)/2)));; a:=Filtered([1..Length(F)],i->F[i]=9); # Muniru A Asiru, Dec 22 2018

[n: n in [2..2600] | &+[d[2]: d in Factorization((n*(n+1)))] eq 10]; // Vincenzo Librandi, Dec 22 2018

Flatten[Position[Accumulate[Range[3500]], _?(PrimeOmega[#]== 9 &)]]
Select[Range[3000], PrimeOmega[(# (# + 1))/2] == 9 &] (* Harvey P. Dale, Jun 22 2017 *)

{ m : A069904(m) = 9 }. - Alois P. Heinz, Aug 05 2019

A320438 Irregular triangle read by rows where T(n,k) is the number of set partitions of {1,...,n} with all block-sums equal to d, where d is the k-th divisor of n*(n+1)/2 that is >= n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 3, 7, 1, 1, 9, 1, 1, 1, 1, 43, 35, 1, 1, 102, 62, 1, 1, 1, 1, 68, 595, 1, 1, 17, 187, 871, 1480, 361, 1, 1, 2650, 657, 1, 1, 9294, 1, 1, 23728, 1, 1, 27763, 4110, 1, 1, 1850, 25035, 108516, 157991, 7636, 1, 1, 11421, 411474, 1

Offset: 1

Gus Wiseman, Jan 08 2019

			Triangle begins:
    1
    1
    1    1
    1    1
    1    1
    1    1
    1    4    1
    1    3    7    1
    1    9    1
    1    1
    1   43   35    1
    1  102   62    1
    1    1
    1   68  595    1
    1   17  187  871 1480  361    1
    1 2650  657    1
Row 8 counts the following set partitions:
  {{18}{27}{36}{45}}  {{1236}{48}{57}}  {{12348}{567}}  {{12345678}}
                      {{138}{246}{57}}  {{12357}{468}}
                      {{156}{237}{48}}  {{12456}{378}}
                                        {{1278}{3456}}
                                        {{1368}{2457}}
                                        {{1458}{2367}}
                                        {{1467}{2358}}

Row lengths are A164978. Row sums are A035470.

Cf. A000110, A000258, A008277, A112956, A164977, A275714, A279375, A300335, A320423, A320424, A321455, A321469.

spsu[,{}]:={{}};spsu[foo,set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@spsu[Select[foo,Complement[#,Complement[set,s]]=={}&],Complement[set,s]]]/@Cases[foo,{i,_}];
Table[Length[spsu[Select[Subsets[Range[n]],Total[#]==d&],Range[n]]],{n,12},{d,Select[Divisors[n*(n+1)/2],#>=n&]}]

More terms from Jinyuan Wang, Feb 27 2025

Name edited by Peter Munn, Mar 06 2025

cp's OEIS Frontend

A035470 Number of ways to break {1,2,3,...,n} into sets with equal sums.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A068443 Triangular numbers which are the product of two primes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

Extensions

A069904 Number of prime factors of n-th triangular number (with multiplicity).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A350593 Numbers k such that tau(k) + tau(k+1) = 6, where tau is the number of divisors function A000005.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

A164978 Number of divisors of n*(n+1)/2 that are >= n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Formula

A112956 a(n) = number of ways the set {1,2,...,n} can be split into proper subsets with equal sums.

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A240527 Indices of 7-almost prime triangular numbers.

Views

Author

Keywords

Examples

Links

Crossrefs