A371449 Numbers whose prime indices are not powers of 2.

1, 5, 11, 13, 17, 23, 25, 29, 31, 37, 41, 43, 47, 55, 59, 61, 65, 67, 71, 73, 79, 83, 85, 89, 97, 101, 103, 107, 109, 113, 115, 121, 125, 127, 137, 139, 143, 145, 149, 151, 155, 157, 163, 167, 169, 173, 179, 181, 185, 187, 191, 193, 197, 199, 205, 211, 215

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.

Links

Table of n, a(n) for n=1..57.

Example

The terms together with their prime indices begin:
     1: {}        85: {3,7}      169: {6,6}     253: {5,9}
     5: {3}       89: {24}       173: {40}      257: {55}
    11: {5}       97: {25}       179: {41}      263: {56}
    13: {6}      101: {26}       181: {42}      269: {57}
    17: {7}      103: {27}       185: {3,12}    271: {58}
    23: {9}      107: {28}       187: {5,7}     275: {3,3,5}
    25: {3,3}    109: {29}       191: {43}      277: {59}
    29: {10}     113: {30}       193: {44}      281: {60}
    31: {11}     115: {3,9}      197: {45}      283: {61}
    37: {12}     121: {5,5}      199: {46}      289: {7,7}
    41: {13}     125: {3,3,3}    205: {3,13}    293: {62}
    43: {14}     127: {31}       211: {47}      295: {3,17}
    47: {15}     137: {33}       215: {3,14}    299: {6,9}
    55: {3,5}    139: {34}       221: {6,7}     305: {3,18}
    59: {17}     143: {5,6}      223: {48}      307: {63}
    61: {18}     145: {3,10}     227: {49}      313: {65}
    65: {3,6}    149: {35}       229: {50}      317: {66}
    67: {19}     151: {36}       233: {51}      319: {5,10}
    71: {20}     155: {3,11}     235: {3,15}    325: {3,3,6}
    73: {21}     157: {37}       239: {52}      331: {67}
    79: {22}     163: {38}       241: {53}      335: {3,19}
    83: {23}     167: {39}       251: {54}      337: {68}

Mathematica

Select[Range[100], And@@Not/@IntegerQ/@Log[2, PrimePi/@First/@FactorInteger[#]]&]

Crossrefs

Partitions of this type are counted by A101417.

For binary indices instead of prime indices we have A326781.

Requiring powers of two gives A318400, for binary indices A253317.

An opposite version is A371443.

For primes instead of powers of 2 we have A320628.

A000040 lists prime numbers, complement A018252.

A000961 lists prime-powers.

A048793 lists binary indices, reverse A272020, length A000120, sum A029931.

A057716 lists non-powers of 2.

A070939 gives length of binary expansion.

A112798 lists prime indices, reverse A296150, length A001222, sum A056239.

Cf. A005117, A326782, A371451, A371444.

Sequence in context: A288450 A346416 A384396 * A272446 A307390 A104110

Adjacent sequences: A371446 A371447 A371448 * A371450 A371451 A371452

Keyword

nonn

Author

Gus Wiseman, Mar 31 2024

Status

approved