This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A371449 #6 Mar 31 2024 23:51:24
%S A371449 1,5,11,13,17,23,25,29,31,37,41,43,47,55,59,61,65,67,71,73,79,83,85,
%T A371449 89,97,101,103,107,109,113,115,121,125,127,137,139,143,145,149,151,
%U A371449 155,157,163,167,169,173,179,181,185,187,191,193,197,199,205,211,215
%N A371449 Numbers whose prime indices are not powers of 2.
%C A371449 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.
%e A371449 The terms together with their prime indices begin:
%e A371449 1: {} 85: {3,7} 169: {6,6} 253: {5,9}
%e A371449 5: {3} 89: {24} 173: {40} 257: {55}
%e A371449 11: {5} 97: {25} 179: {41} 263: {56}
%e A371449 13: {6} 101: {26} 181: {42} 269: {57}
%e A371449 17: {7} 103: {27} 185: {3,12} 271: {58}
%e A371449 23: {9} 107: {28} 187: {5,7} 275: {3,3,5}
%e A371449 25: {3,3} 109: {29} 191: {43} 277: {59}
%e A371449 29: {10} 113: {30} 193: {44} 281: {60}
%e A371449 31: {11} 115: {3,9} 197: {45} 283: {61}
%e A371449 37: {12} 121: {5,5} 199: {46} 289: {7,7}
%e A371449 41: {13} 125: {3,3,3} 205: {3,13} 293: {62}
%e A371449 43: {14} 127: {31} 211: {47} 295: {3,17}
%e A371449 47: {15} 137: {33} 215: {3,14} 299: {6,9}
%e A371449 55: {3,5} 139: {34} 221: {6,7} 305: {3,18}
%e A371449 59: {17} 143: {5,6} 223: {48} 307: {63}
%e A371449 61: {18} 145: {3,10} 227: {49} 313: {65}
%e A371449 65: {3,6} 149: {35} 229: {50} 317: {66}
%e A371449 67: {19} 151: {36} 233: {51} 319: {5,10}
%e A371449 71: {20} 155: {3,11} 235: {3,15} 325: {3,3,6}
%e A371449 73: {21} 157: {37} 239: {52} 331: {67}
%e A371449 79: {22} 163: {38} 241: {53} 335: {3,19}
%e A371449 83: {23} 167: {39} 251: {54} 337: {68}
%t A371449 Select[Range[100],And@@Not/@IntegerQ/@Log[2, PrimePi/@First/@FactorInteger[#]]&]
%Y A371449 Partitions of this type are counted by A101417.
%Y A371449 For binary indices instead of prime indices we have A326781.
%Y A371449 Requiring powers of two gives A318400, for binary indices A253317.
%Y A371449 An opposite version is A371443.
%Y A371449 For primes instead of powers of 2 we have A320628.
%Y A371449 A000040 lists prime numbers, complement A018252.
%Y A371449 A000961 lists prime-powers.
%Y A371449 A048793 lists binary indices, reverse A272020, length A000120, sum A029931.
%Y A371449 A057716 lists non-powers of 2.
%Y A371449 A070939 gives length of binary expansion.
%Y A371449 A112798 lists prime indices, reverse A296150, length A001222, sum A056239.
%Y A371449 Cf. A005117, A326782, A371451, A371444.
%K A371449 nonn
%O A371449 1,2
%A A371449 _Gus Wiseman_, Mar 31 2024