A358137 -id:A358137 - cp's OEIS frontend

A359674 Zero-based weighted sum of the prime indices of n in weakly increasing order.

0, 0, 0, 1, 0, 2, 0, 3, 2, 3, 0, 5, 0, 4, 3, 6, 0, 6, 0, 7, 4, 5, 0, 9, 3, 6, 6, 9, 0, 8, 0, 10, 5, 7, 4, 11, 0, 8, 6, 12, 0, 10, 0, 11, 8, 9, 0, 14, 4, 9, 7, 13, 0, 12, 5, 15, 8, 10, 0, 14, 0, 11, 10, 15, 6, 12, 0, 15, 9, 11, 0, 17, 0, 12, 9, 17, 5, 14, 0, 18

Offset: 1

Gus Wiseman, Jan 13 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

The zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.

			The prime indices of 12 are {1,1,2}, so a(12) = 0*1 + 1*1 + 2*2 = 5.

Positions of last appearances (except 0) are A001248.
Positions of 0's are A008578.
The version for standard compositions is A124757, reverse A231204.
The one-based version is A304818, reverse A318283.
Positions of first appearances are A359675, reverse A359680.
First position of n is A359676(n), reverse A359681.
The reverse version is A359677, firsts A359679.
Number of appearances of positive n is A359678(n).
A053632 counts compositions by zero-based weighted sum.
A112798 lists prime indices, length A001222, sum A056239.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Cf. A029931, A055932, A243055, A359043, A358194, A359360, A359497, A359681, A359682, A359755.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
wts[y_]:=Sum[(i-1)*y[[i]],{i,Length[y]}];
Table[wts[primeMS[n]],{n,100}]

A261079 Sum of index differences between prime factors of n, summed over all unordered pairs of primes present (with multiplicity) in the prime factorization of n.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 3, 1, 0, 0, 2, 0, 4, 2, 4, 0, 3, 0, 5, 0, 6, 0, 4, 0, 0, 3, 6, 1, 4, 0, 7, 4, 6, 0, 6, 0, 8, 2, 8, 0, 4, 0, 4, 5, 10, 0, 3, 2, 9, 6, 9, 0, 7, 0, 10, 4, 0, 3, 8, 0, 12, 7, 6, 0, 6, 0, 11, 2, 14, 1, 10, 0, 8, 0, 12, 0, 10, 4, 13, 8, 12, 0, 6, 2, 16, 9, 14, 5, 5, 0, 6, 6, 8, 0, 12, 0, 15, 4, 15, 0, 6, 0, 8, 10, 12, 0, 14, 6, 18, 8, 16, 3, 10

Offset: 1

Antti Karttunen, Sep 23 2015

nonn

			For n = 1 the prime factorization is empty, thus there is nothing to sum, so a(1) = 0.
For n = 6 = 2*3 = prime(1) * prime(2), a(6) = 1 because the (absolute value of) difference between prime indices of 2 and 3 is 1.
For n = 10 = 2*5 = prime(1) * prime(3), a(10) = 2 because the difference between prime indices of 2 and 5 is 2.
For n = 12 = 2*2*3 = prime(1) * prime(1) * prime(2), a(12) = 2 because the difference between prime indices of 2 and 3 is 1, and the pair (2,3) occurs twice as one can pick either one of the two 2's present in the prime factorization to be a pair of a single 3. Note that the index difference between 2 and 2 is 0, thus the pair (2,2) of prime divisors does not contribute to the sum.
For n = 36 = 2*2*3*3, a(36) = 4 because the index difference between 2 and 3 is 1, and the prime factor pair (2,3) occurs 2^2 = four times in total. As the index difference is zero between 2 and 2 as well as between 3 and 3, the pairs (2,2) and (3,3) do not contribute to the sum.

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from indices in prime factorization

Cf. A000720.
Cf. A000961 (positions of zeros), A006094 (positions of ones).
Cf. A243055, A242411.
Cf. also A260737.
A055396 gives minimum prime index, maximum A061395.
A112798 list prime indices, length A001222, sum A056239.
A304818 adds up partial sums of reversed prime indices, row sums of A359361.
A318283 adds up partial sums of prime indices, row sums of A358136.
Cf. A029931, A316413, A325362, A326836, A326844, A355536, A358137, A359362.

Table[Function[p, Total@ Map[Function[b, Times @@ {First@ Differences@ PrimePi@ b, Count[Subsets[p, {2}], c_ /; SameQ[c, b]]}], Subsets[Union@ p, {2}]]][Flatten@ Replace[FactorInteger@ n, {p_, e_} :> ConstantArray[p, e], 2]], {n, 120}] (* Michael De Vlieger, Mar 08 2017 *)

a(n) = A304818(n) - A318283(n). - Gus Wiseman, Jan 09 2023

a(n) = 2*A304818(n) - A359362(n). - Gus Wiseman, Jan 09 2023

A359676 Least positive integer whose weakly increasing prime indices have zero-based weighted sum n (A359674).

Original entry on oeis.org

1, 4, 6, 8, 14, 12, 16, 20, 30, 24, 32, 36, 40, 52, 48, 56, 100, 72, 80, 92, 96, 104, 112, 124, 136, 148, 176, 152, 214, 172, 184, 188, 262, 212, 272, 236, 248, 244, 304, 268, 346, 284, 328, 292, 386, 316, 398, 332, 376, 356, 458, 388, 478, 404, 472, 412, 526

Offset: 1

Gus Wiseman, Jan 14 2023

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

The zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.

			The terms together with their prime indices begin:
    1: {}
    4: {1,1}
    6: {1,2}
    8: {1,1,1}
   14: {1,4}
   12: {1,1,2}
   16: {1,1,1,1}
   20: {1,1,3}
   30: {1,2,3}
   24: {1,1,1,2}
   32: {1,1,1,1,1}
   36: {1,1,2,2}
   40: {1,1,1,3}
   52: {1,1,6}
   48: {1,1,1,1,2}

First position of n in A359674, reverse A359677.
The sorted version is A359675, reverse A359680.
The reverse one-based version is A359679, sorted A359754.
The reverse version is A359681.
The one-based version is A359682, sorted A359755.
The version for standard compositions is A359756, one-based A089633.
A053632 counts compositions by zero-based weighted sum.
A112798 lists prime indices, length A001222, sum A056239.
A124757 gives zero-based weighted sum of standard compositions, rev A231204.
A304818 gives weighted sums of prime indices, reverse A318283.
A320387 counts multisets by weighted sum, zero-based A359678.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Cf. A001248, A029931, A055932, A243055, A359043, A358194, A359497, A359683.

nn=20;
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
wts[y_]:=Sum[(i-1)*y[[i]],{i,Length[y]}];
seq=Table[wts[primeMS[n]],{n,1,Prime[nn]^2}];
Table[Position[seq,k][[1,1]],{k,0,nn}]

A359677 Zero-based weighted sum of the reversed (weakly decreasing) prime indices of n.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 3, 0, 1, 2, 6, 0, 4, 0, 3, 2, 1, 0, 6, 3, 1, 6, 3, 0, 4, 0, 10, 2, 1, 3, 7, 0, 1, 2, 6, 0, 4, 0, 3, 6, 1, 0, 10, 4, 5, 2, 3, 0, 9, 3, 6, 2, 1, 0, 7, 0, 1, 6, 15, 3, 4, 0, 3, 2, 5, 0, 11, 0, 1, 7, 3, 4, 4, 0, 10, 12, 1, 0, 7, 3

Offset: 1

Gus Wiseman, Jan 13 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

The zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.

			The reversed prime indices of 12 are (2,1,1), so a(12) = 0*2 + 1*1 + 2*1 = 3.

Positions of 0's are A008578.
Positions of 1's are A100484.
The version for standard compositions is A231204, reverse of A124757.
The one-based version is A318283, unreversed A304818.
The one-based version for standard compositions is A359042, rev of A029931.
This is the reverse version of A359674.
First position of n is A359679(n), reverse of A359675.
Positions of first appearances are A359680, reverse of A359676.
A053632 counts compositions by weighted sum.
A112798 lists prime indices, length A001222, sum A056239.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Cf. A001248, A055932, A243055, A359043, A358194, A359678, A359681, A359683, A359754, A359755.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
wts[y_]:=Sum[(i-1)*y[[i]],{i,Length[y]}];
Table[wts[Reverse[primeMS[n]]],{n,100}]

A359682 Least positive integer whose weakly increasing prime indices have weighted sum (A304818) equal to n.

Original entry on oeis.org

1, 2, 3, 4, 7, 6, 8, 10, 15, 12, 16, 18, 20, 26, 24, 28, 50, 36, 40, 46, 48, 52, 56, 62, 68, 74, 88, 76, 107, 86, 92, 94, 131, 106, 136, 118, 124, 122, 152, 134, 173, 142, 164, 146, 193, 158, 199, 166, 188, 178, 229, 194, 239, 202, 236, 206, 263, 214, 271, 218

Offset: 0

Gus Wiseman, Jan 15 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

The weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i.

			The 5 numbers with weighted sum of prime indices 12, together with their prime indices:
  20: {1,1,3}
  27: {2,2,2}
  33: {2,5}
  37: {12}
  49: {4,4}
Hence a(12) = 20.

The version for standard compositions is A089633, zero-based A359756.
First position of n in A304818, reverse A318283.
The greatest instead of least is A359497, reverse A359683.
The sorted zero-based version is A359675, reverse A359680.
The zero-based version is A359676, reverse A359681.
The reverse version is A359679.
The sorted version is  A359755, reverse A359754.
A112798 lists prime indices, length A001222, sum A056239.
A320387 counts multisets by weighted sum, zero-based A359678.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Cf. A001248, A029931, A055932, A243055, A359043, A358194, A359360.

nn=20;
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
ots[y_]:=Sum[i*y[[i]],{i,Length[y]}];
seq=Table[ots[primeMS[n]],{n,1,Prime[nn]^2}];
Table[Position[seq,k][[1,1]],{k,0,nn}]

A359497 Greatest positive integer whose weakly increasing prime indices have weighted sum (A304818) equal to n.

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 13, 17, 19, 25, 29, 35, 49, 55, 77, 121, 91, 143, 169, 187, 221, 289, 247, 323, 361, 391, 437, 539, 605, 847, 1331, 715, 1001, 1573, 1183, 1859, 2197, 1547, 2431, 2873, 3179, 3757, 4913, 3553, 4199, 5491, 4693, 6137, 6859, 9317, 14641

Offset: 0

Gus Wiseman, Jan 15 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

The weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i.

			The terms together with their prime indices begin:
    1: {}
    2: {1}
    3: {2}
    5: {3}
    7: {4}
   11: {5}
   13: {6}
   17: {7}
   19: {8}
   25: {3,3}
   29: {10}
   35: {3,4}
   49: {4,4}
   55: {3,5}
   77: {4,5}
The 5 numbers with weighted sum of prime indices 12, together with their prime indices:
  20: {1,1,3}
  27: {2,2,2}
  33: {2,5}
  37: {12}
  49: {4,4}
Hence a(12) = 49.

Andrew Howroyd, Table of n, a(n) for n = 0..500

First position of n in A304818, reverse A318283.
The least instead of greatest is given by A359682, reverse A359679.
The reverse version is A359683.
A112798 lists prime indices, length A001222, sum A056239.
A320387 counts multisets by weighted sum, zero-based A359678.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Cf. A001248, A029931, A055932, A089633, A243055, A358194, A359043, A359676, A359681, A359755.

nn=10;
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
ots[y_]:=Sum[i*y[[i]],{i,Length[y]}];
seq=Table[ots[primeMS[n]],{n,1,2^nn}];
Table[Position[seq,k][[-1,1]],{k,0,nn}]

a(n)={ my(recurse(r, k, m) = if(k==1, if(m>=r, prime(r)),
  my(z=0); for(j=1, min(m, (r-k*(k-1)/2)\k), z=max(z, self()(r-k*j, k-1, j)*prime(j))); z));
  if(n==0, 1, vecmax(vector((sqrtint(8*n+1)-1)\2, k, recurse(n, k, n))));
} \\ Andrew Howroyd, Jan 21 2023

Terms a(21) and beyond from Andrew Howroyd, Jan 21 2023

A359679 Least number with weighted sum of reversed (weakly decreasing) prime indices (A318283) equal to n.

Original entry on oeis.org

1, 2, 3, 4, 6, 10, 8, 12, 19, 18, 16, 24, 27, 36, 43, 32, 48, 59, 61, 67, 71, 64, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269

Offset: 0

Gus Wiseman, Jan 14 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

The weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i.

			12 has reversed prime indices (2,1,1), with weighted sum 7, and no number < 12 has the same weighted sum of reversed prime indices, so a(7) = 12.

The version for standard compositions is A089633, zero-based A359756.
First position of n in A318283, unreversed A304818.
The unreversed zero-based version is A359676.
The sorted zero-based version is A359680, unreversed A359675.
The zero-based version is A359681.
The unreversed version is A359682.
The greatest instead of least is A359683, unreversed A359497.
The sorted version is A359754, unreversed A359755.
A112798 lists prime indices, length A001222, sum A056239.
A320387 counts multisets by weighted sum, zero-based A359678.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Cf. A001248, A029931, A053632, A055932, A231204, A243055, A359043, A358194, A359360, A359677.

nn=20;
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
ots[y_]:=Sum[i*y[[i]],{i,Length[y]}];
seq=Table[ots[Reverse[primeMS[n]]],{n,1,Prime[nn]^2}];
Table[Position[seq,k][[1,1]],{k,0,nn}]

A359675 Positions of first appearances in the sequence of zero-based weighted sums of prime indices (A359674).

Original entry on oeis.org

1, 4, 6, 8, 12, 14, 16, 20, 24, 30, 32, 36, 40, 48, 52, 56, 72, 80, 92, 96, 100, 104, 112, 124, 136, 148, 152, 172, 176, 184, 188, 212, 214, 236, 244, 248, 262, 268, 272, 284, 292, 304, 316, 328, 332, 346, 356, 376, 386, 388, 398, 404, 412, 428, 436, 452, 458

Offset: 1

Gus Wiseman, Jan 13 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

The zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.

			The terms together with their prime indices begin:
   1: {}
   4: {1,1}
   6: {1,2}
   8: {1,1,1}
  12: {1,1,2}
  14: {1,4}
  16: {1,1,1,1}
  20: {1,1,3}
  24: {1,1,1,2}
  30: {1,2,3}
  32: {1,1,1,1,1}
  36: {1,1,2,2}
  40: {1,1,1,3}
  48: {1,1,1,1,2}

Positions of first appearances in A359674.
The unsorted version A359676.
The reverse version is A359680, unsorted A359681.
The reverse one-based version is A359754, unsorted A359679.
The one-based version is A359755, unsorted A359682.
The version for standard compositions is A359756, one-based A089633.
A053632 counts compositions by zero-based weighted sum.
A112798 lists prime indices, length A001222, sum A056239.
A124757 gives zero-based weighted sum of standard compositions, rev A231204.
A304818 gives weighted sum of prime indices, reverse A318283.
A320387 counts multisets by weighted sum, zero-based A359678.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Cf. A001248, A029931, A055932, A243055, A359043, A358194, A359360, A359497, A359677, A359683.

nn=100;
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
wts[y_]:=Sum[(i-1)*y[[i]],{i,Length[y]}];
seq=Table[wts[primeMS[n]],{n,1,nn}];
Select[Range[nn],FreeQ[seq[[Range[#-1]]],seq[[#]]]&]

A359680 Positions of first appearances in the sequence of zero-based weighted sums of reversed prime indices (A359677).

Original entry on oeis.org

1, 4, 8, 9, 16, 18, 32, 36, 50, 54, 64, 72, 81, 100, 108, 128, 144, 216, 243, 256, 288, 300, 400, 432, 486, 512, 576, 600, 648, 729, 800, 864, 1024, 1152, 1296, 1350, 1728, 1944, 2048, 2187, 2304, 2400, 2916, 3375, 3456, 3600, 4096, 4374, 4608, 4800, 5184

Offset: 1

Gus Wiseman, Jan 15 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

The zero-based weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} (i-1)*y_i.

			The terms together with their prime indices begin:
     1: {}
     4: {1,1}
     8: {1,1,1}
     9: {2,2}
    16: {1,1,1,1}
    18: {1,2,2}
    32: {1,1,1,1,1}
    36: {1,1,2,2}
    50: {1,3,3}
    54: {1,2,2,2}
    64: {1,1,1,1,1,1}
    72: {1,1,1,2,2}
    81: {2,2,2,2}
   100: {1,1,3,3}
   108: {1,1,2,2,2}
   128: {1,1,1,1,1,1,1}

The unreversed version is A359675, unsorted A359676.
Positions of first appearances in A359677, unreversed A359674.
This is the sorted version of A359681.
The one-based version is A359754, unsorted A359679.
The unreversed one-based version is A359755, unsorted A359682.
The version for standard compositions is A359756, one-based A089633.
A053632 counts compositions by zero-based weighted sum.
A112798 lists prime indices, length A001222, sum A056239, reverse A296150.
A124757 gives zero-based weighted sums of standard compositions, rev A231204.
A304818 gives weighted sum of prime indices, reverse A318283.
A320387 counts multisets by weighted sum, zero-based A359678.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Cf. A029931, A055932, A243055, A358194, A359043, A359683.

nn=1000;
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
wts[y_]:=Sum[(i-1)*y[[i]],{i,Length[y]}];
seq=Table[wts[Reverse[primeMS[n]]],{n,1,nn}];
Select[Range[nn],FreeQ[seq[[Range[#-1]]],seq[[#]]]&]

A359683 Greatest positive integer whose reversed (weakly decreasing) prime indices have weighted sum (A318283) equal to n.

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 14, 22, 26, 34, 44, 55, 68, 85, 110, 130, 170, 190, 242, 290, 374, 418, 506, 638, 748, 836, 1012, 1276, 1364, 1628, 1914, 2090, 2552, 3190, 3410, 4070, 4510, 5060, 6380, 7018, 8140, 9020, 9922, 11396, 14036, 15004, 17908, 19844, 21692, 23452

Offset: 0

Gus Wiseman, Jan 15 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

The weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i.

			The terms together with their prime indices begin:
      1: {}
      2: {1}
      3: {2}
      5: {3}
      7: {4}
     11: {5}
     14: {1,4}
     22: {1,5}
     26: {1,6}
     34: {1,7}
     44: {1,1,5}
     55: {3,5}
     68: {1,1,7}
     85: {3,7}
    110: {1,3,5}
    130: {1,3,6}
    170: {1,3,7}
    190: {1,3,8}
    242: {1,5,5}
    290: {1,3,10}
The 6 numbers with weighted sum of reversed prime indices 9, together with their prime indices:
  18: {1,2,2}
  23: {9}
  25: {3,3}
  28: {1,1,4}
  33: {2,5}
  34: {1,7}
Hence a(9) = 34.

First position of n in A318283, unreversed A304818.
The unreversed version is A359497.
The least instead of greatest is A359679, unreversed A359682.
A112798 lists prime indices, length A001222, sum A056239.
A320387 counts multisets by weighted sum, zero-based A359678.
A358136 lists partial sums of prime indices, ranked by A358137, rev A359361.
Cf. A001248, A029931, A055932, A089633, A243055, A358194, A359043, A359676, A359681, A359755.

nn=10;
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
ots[y_]:=Sum[i*y[[i]],{i,Length[y]}];
seq=Table[ots[Reverse[primeMS[n]]],{n,1,2^nn}];
Table[Position[seq,k][[-1,1]],{k,0,nn}]

More terms from Jinyuan Wang, Jan 26 2023

cp's OEIS Frontend

A359674 Zero-based weighted sum of the prime indices of n in weakly increasing order.

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A261079 Sum of index differences between prime factors of n, summed over all unordered pairs of primes present (with multiplicity) in the prime factorization of n.

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Formula

A359676 Least positive integer whose weakly increasing prime indices have zero-based weighted sum n (A359674).

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A359677 Zero-based weighted sum of the reversed (weakly decreasing) prime indices of n.

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A359682 Least positive integer whose weakly increasing prime indices have weighted sum (A304818) equal to n.

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A359497 Greatest positive integer whose weakly increasing prime indices have weighted sum (A304818) equal to n.

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A359679 Least number with weighted sum of reversed (weakly decreasing) prime indices (A318283) equal to n.

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A359675 Positions of first appearances in the sequence of zero-based weighted sums of prime indices (A359674).

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A359680 Positions of first appearances in the sequence of zero-based weighted sums of reversed prime indices (A359677).

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