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A302796 Squarefree numbers whose prime indices are relatively prime. Nonprime Heinz numbers of strict integer partitions with relatively prime parts. 26
1, 2, 6, 10, 14, 15, 22, 26, 30, 33, 34, 35, 38, 42, 46, 51, 55, 58, 62, 66, 69, 70, 74, 77, 78, 82, 85, 86, 93, 94, 95, 102, 105, 106, 110, 114, 118, 119, 122, 123, 130, 134, 138, 141, 142, 143, 145, 146, 154, 155, 158, 161, 165, 166, 170, 174, 177, 178, 182 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A prime index of n is a number m such that prime(m) divides n. Two or more numbers are relatively prime if they have no common divisor other than 1. A single number is not considered relatively prime unless it is equal to 1.

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

Sequence of terms together with their sets of prime indices begins:

01 : {}

02 : {1}

06 : {1,2}

10 : {1,3}

14 : {1,4}

15 : {2,3}

22 : {1,5}

26 : {1,6}

30 : {1,2,3}

33 : {2,5}

34 : {1,7}

35 : {3,4}

38 : {1,8}

42 : {1,2,4}

46 : {1,9}

51 : {2,7}

55 : {3,5}

58 : {1,10}

62 : {1,11}

66 : {1,2,5}

MATHEMATICA

Select[Range[100], Or[#===1, SquareFreeQ[#]&&GCD@@PrimePi/@FactorInteger[#][[All, 1]]===1]&]

PROG

(PARI) isok(n) = {if (n == 1, return (1)); if (issquarefree(n), my(f = factor(n)); return (gcd(vector(#f~, k, primepi(f[k, 1]))) == 1); ); } \\ Michel Marcus, Apr 13 2018

CROSSREFS

Cf. A001222, A003963, A005117, A007359, A051424, A056239, A275024, A289509, A302242, A302505, A302696, A302697, A302698, A302797, A302798.

Sequence in context: A281974 A080324 A165562 * A302797 A130319 A191256

Adjacent sequences:  A302793 A302794 A302795 * A302797 A302798 A302799

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 13 2018

STATUS

approved

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Last modified January 20 19:53 EST 2020. Contains 331096 sequences. (Running on oeis4.)