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A374536
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a(n) is the least exponentially odd number that is nonsquarefree and is followed by exactly n successive exponentially odd numbers that are squarefree, or -1 if no such number exists.
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1
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135, 24, 120, 27, 96, 88, 32, 40, 328, 168, 136, 104, 1288, 1161, 352, 488, 8, 783, 189, 952, 4520, 56, 11576, 67384, 5088, 1336, 35768, 16173, 53768, 80328, 128169, 28576, 247375, 208552, 2556192, 1486568, 3099368, 1653032, 910568, 7864008, 34242976, 14484152
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OFFSET
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0,1
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LINKS
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FORMULA
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EXAMPLE
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a(0) = 135 because 135 and 136 are successive nonsquarefree exponentially odd numbers with no squarefree number between them.
a(1) = 24 because 24 and 27 are successive nonsquarefree exponentially odd numbers with one squarefree number between them, 26.
a(2) = 120 because 120 and 125 are successive nonsquarefree exponentially odd numbers with two squarefree number between them, 122 and 123.
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MATHEMATICA
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sq[k_] := Module[{e = FactorInteger[k][[;; , 2]]}, If[AnyTrue[e, EvenQ], 0, If[k == 1 || Max[e] == 1, 2, 1]]]; seq[len_, kmax_ : Infinity] := Module[{v = Table[0, {len}], c = 0, k = 1, k0 = 0, m, i = 1}, While[c < len && k < kmax, m = sq[k]; If[m > 0, If[m == 2, i++, If[k0 > 0, If[i <= len && v[[i]] == 0, c++; v[[i]] = k0]; i = 1]; k0 = k]]; k++]; v]; seq[10]
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PROG
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(PARI) issq(k) = {my(e = factor(k)[, 2]); for(i = 1, #e, if(!(e[i] % 2), return(0))); if(k == 1 || vecmax(e) == 1, 2, 1); }
lista(len, kmax = oo) = {my(v = vector(len), c = 0, k = 1, k0 = 0, m, i = 1); while(c < len && k < kmax, m = issq(k); if(m > 0, if(m == 2, i++, if(k0 > 0, if(i <= len && v[i] == 0, c++; v[i] = k0); i = 1); k0 = k)); k++); v; }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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