A340608 The number of prime factors of n (A001222) is relatively prime to the maximum prime index of n (A061395).

2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 19, 22, 23, 25, 27, 28, 29, 31, 32, 33, 34, 37, 40, 41, 42, 43, 44, 46, 47, 48, 51, 53, 55, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 79, 80, 82, 83, 85, 88, 89, 90, 93, 94, 97, 98, 99

Offset: 1

Author

Gus Wiseman, Jan 27 2021

Keywords

• nonn

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.

Examples

			The sequence of terms together with their prime indices begins:
     2: {1}          22: {1,5}          44: {1,1,5}
     3: {2}          23: {9}            46: {1,9}
     4: {1,1}        25: {3,3}          47: {15}
     5: {3}          27: {2,2,2}        48: {1,1,1,1,2}
     7: {4}          28: {1,1,4}        51: {2,7}
     8: {1,1,1}      29: {10}           53: {16}
    10: {1,3}        31: {11}           55: {3,5}
    11: {5}          32: {1,1,1,1,1}    59: {17}
    12: {1,1,2}      33: {2,5}          60: {1,1,2,3}
    13: {6}          34: {1,7}          61: {18}
    15: {2,3}        37: {12}           62: {1,11}
    16: {1,1,1,1}    40: {1,1,1,3}      63: {2,2,4}
    17: {7}          41: {13}           64: {1,1,1,1,1,1}
    18: {1,2,2}      42: {1,2,4}        66: {1,2,5}
    19: {8}          43: {14}           67: {19}
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Note: Heinz numbers are given in parentheses below.

These are the Heinz numbers of the partitions counted by A200750.

The case of equality is A047993 (A106529).

The divisible instead of coprime version is A168659 (A340609).

The dividing instead of coprime version is A168659 (A340610), with strict case A340828 (A340856).

A001222 counts prime factors.

A006141 counts partitions whose length equals their minimum (A324522).

A051424 counts singleton or pairwise coprime partitions (A302569).

A056239 adds up prime indices.

A061395 selects the maximum prime index.

A067538 counts partitions whose length divides their sum (A316413).

A067538 counts partitions whose maximum divides their sum (A326836).

A112798 lists the prime indices of each positive integer.

A259936 counts singleton or pairwise coprime factorizations.

A325134 = A001222 + A061395.

A326845 = A056239 * A061395.

A326849 counts partitions whose sum divides length times maximum (A326848).

A327516 counts pairwise coprime partitions (A302696).

Cf. A003114, A039900, A096401, A244990/A244991, A340606, A340653, A340691, A340787/A340788.

Programs

Mathematica

Select[Range[100],GCD[PrimeOmega[#],PrimePi[FactorInteger[#][[-1,1]]]]==1&]