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.
EXAMPLE
The sequence of terms together with the corresponding sets of multisets begins:
1: {} 91: {{1,1},{1,2}} 173: {{1,1,1,3}}
7: {{1,1}} 97: {{3,3}} 181: {{1,2,4}}
13: {{1,2}} 101: {{1,6}} 193: {{1,1,5}}
19: {{1,1,1}} 103: {{2,2,2}} 197: {{2,2,3}}
23: {{2,2}} 107: {{1,1,4}} 199: {{1,9}}
29: {{1,3}} 113: {{1,2,3}} 203: {{1,1},{1,3}}
37: {{1,1,2}} 131: {{1,1,1,1,1}} 223: {{1,1,1,1,2}}
43: {{1,4}} 133: {{1,1},{1,1,1}} 227: {{4,4}}
47: {{2,3}} 137: {{2,5}} 229: {{1,3,3}}
53: {{1,1,1,1}} 139: {{1,7}} 233: {{2,7}}
61: {{1,2,2}} 149: {{3,4}} 239: {{1,1,6}}
71: {{1,1,3}} 151: {{1,1,2,2}} 247: {{1,2},{1,1,1}}
73: {{2,4}} 161: {{1,1},{2,2}} 251: {{1,2,2,2}}
79: {{1,5}} 163: {{1,8}} 257: {{3,5}}
89: {{1,1,1,2}} 167: {{2,6}} 259: {{1,1},{1,1,2}}
MATHEMATICA
Select[Range[1, 100, 2], SquareFreeQ[#]&&FreeQ[If[#==1, {}, FactorInteger[#]], {p_, k_}/; PrimeQ[PrimePi[p]]]&]
CROSSREFS
These primes (of nonprime index) are listed by A007821.
The not necessarily odd version is A340104.
The prime instead of odd nonprime version:
primes: A006450
products: A076610
strict: A302590
The squarefree semiprime instead of odd nonprime version:
strict: A309356
primes: A322551
products: A339113
The semiprime instead of odd nonprime version:
primes: A106349
products: A339112
strict: A340020
A001358 lists semiprimes.
A257994 counts prime prime indices.
A302242 is the weight of the multiset of multisets with MM-number n.
A305079 is the number of connected components for MM-number n.
A330944 counts nonprime prime indices.
A339561 lists products of distinct squarefree semiprimes.
MM-numbers: A255397 (normal), A302478 (set multisystems), A320630 (set multipartitions), A302494 (sets of sets), A305078 (connected), A316476 (antichains), A318991 (chains), A320456 (covers), A328514 (connected sets of sets), A329559 (clutters), A340019 (half-loop graphs).
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 12 2021
STATUS
approved