A340608 - OEIS

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

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OFFSET

1,1

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

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

EXAMPLE

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}

MATHEMATICA

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

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.

Sequence in context: A039152 A051705 A039082 * A047503 A228803 A037014

Adjacent sequences: A340605 A340606 A340607 * A340609 A340610 A340611

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 27 2021

STATUS

approved