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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).
4
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
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]));
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.
Sequence in context: A046158 A070274 A088968 * A057924 A103538 A144671
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 17 2019
STATUS
approved