A328451 Sorted positions of first appearances in A328219, where if n = A000040(i_1) * ... * A000040(i_k), then A328219(n) = LCM(1+i_1,...,1+i_k).

1, 2, 3, 5, 6, 7, 13, 14, 15, 17, 19, 21, 26, 29, 35, 37, 38, 39, 42, 47, 51, 53, 58, 61, 65, 74, 78, 79, 87, 89, 91, 95, 101, 105, 106, 107, 111, 113, 119, 122, 127, 133, 141, 145, 151, 158, 159, 173, 174, 178, 181, 182, 183, 185, 195, 199, 202, 203, 214, 221

Offset

1,2

Comments

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.

Indices of 1's in the ordinal transform of A328219. - Antti Karttunen, Oct 18 2019

Links

Table of n, a(n) for n=1..60.

Example

The sequence of terms together with their prime indices begins:
   1: {}
   2: {1}
   3: {2}
   5: {3}
   6: {1,2}
   7: {4}
  13: {6}
  14: {1,4}
  15: {2,3}
  17: {7}
  19: {8}
  21: {2,4}
  26: {1,6}
  29: {10}
  35: {3,4}
  37: {12}
  38: {1,8}
  39: {2,6}
  42: {1,2,4}
  47: {15}

Mathematica

dav=Table[If[n==1, 1, LCM@@(PrimePi/@First/@FactorInteger[n]+1)], {n, 100}];
Table[Position[dav, i][[1, 1]], {i, dav//.{A___, x_, B___, x_, C___}:>{A, x, B, C}}]

Prog

(PARI)
up_to = 1024;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A290103(n) = lcm(apply(p->primepi(p), factor(n)[, 1]));
A328219(n) = A290103(A003961(n));
vord_trans = ordinal_transform(vector(up_to, n, A328219(n)));
for(n=1, up_to, if(1==vord_trans[n], print1(n, ", "))); \\ Antti Karttunen, Oct 18 2019

Crossrefs

A subsequence of A005117.

Sorted positions of first appearances in A328219.

The GCD of the prime indices of n, all plus 1, is A328169(n).

The LCM of the prime indices of n, all minus 1, is A328456(n).

Partitions whose parts plus 1 are relatively prime are A318980.

Numbers whose prime indices plus 1 are relatively prime are A318981.

Cf. A001222, A056239, A112798, A289508, A289509, A290103, A328163, A328167, A328168, A328170.

Sequence in context: A046158 A070274 A088968 * A057924 A103538 A144671

Adjacent sequences: A328448 A328449 A328450 * A328452 A328453 A328454

Keyword

nonn

Author

Gus Wiseman, Oct 17 2019

Status

approved