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 A328335 Numbers whose consecutive prime indices are relatively prime. 8
 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 22, 23, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 48, 51, 52, 53, 55, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First differs from A302569 in having 105, which has prime indices {2, 3, 4}. 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. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of partitions whose consecutive parts are relatively prime (A328172). LINKS EXAMPLE The sequence of terms together with their prime indices begins:    1: {}    2: {1}    3: {2}    4: {1,1}    5: {3}    6: {1,2}    7: {4}    8: {1,1,1}   10: {1,3}   11: {5}   12: {1,1,2}   13: {6}   14: {1,4}   15: {2,3}   16: {1,1,1,1}   17: {7}   19: {8}   20: {1,1,3}   22: {1,5}   23: {9} MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[100], !MatchQ[primeMS[#], {___, x_, y_, ___}/; GCD[x, y]>1]&] CROSSREFS A superset of A302569. Numbers whose prime indices are relatively prime are A289509. Numbers with no consecutive prime indices relatively prime are A328336. Cf. A000837, A056239, A112798, A281116, A289508, A318981, A328168, A328169, A328172, A328187, A328188, A328220. Sequence in context: A325389 A020662 A306202 * A302569 A235034 A107037 Adjacent sequences:  A328332 A328333 A328334 * A328336 A328337 A328338 KEYWORD nonn AUTHOR Gus Wiseman, Oct 14 2019 STATUS approved

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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)