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A276937 Numbers n with at least one prime factor prime(k) such that prime(k)^k is a divisor of n, but with no factor prime(j) such that prime(j)^(j+1) divides n. 5
2, 6, 9, 10, 14, 18, 22, 26, 30, 34, 38, 42, 45, 46, 50, 58, 62, 63, 66, 70, 74, 78, 82, 86, 90, 94, 98, 99, 102, 106, 110, 114, 117, 118, 122, 125, 126, 130, 134, 138, 142, 146, 150, 153, 154, 158, 166, 170, 171, 174, 178, 182, 186, 190, 194, 198, 202, 206, 207, 210, 214, 218, 222, 225, 226, 230, 234, 238, 242, 246, 250 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n for which A276077(n)=0 and A276935(n) > 0.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..5000

EXAMPLE

14 = 2*7 = prime(1)^1 * prime(4)^1 is a member as the first prime factor (2) satisfies the first condition, and neither prime factor violates the second condition.

36 = 4*9 = prime(1)^2 * prime(2)^2 is NOT a member because prime(1)^2 does not satisfy the second condition.

45 = 5*9 = prime(3)^1 * prime(2)^2 is a member as the latter prime factor satisfies the first condition, and neither prime factor violates the second condition.

MATHEMATICA

p[n_]:=FactorInteger[n][[All, 1]]; f[n_]:=PrimePi/@p[n];

yQ[n_]:=Select[n/(Prime[f[n]]^f[n]), IntegerQ]!={};

nQ[n_]:=Select[n/(Prime[f[n]]^(f[n]+1)), IntegerQ]=={};

Select[Range[2, 250], yQ[#]&&nQ[#]&] (* Ivan N. Ianakiev, Sep 28 2016 *)

PROG

(Scheme, with Antti Karttunen's IntSeq-library)

(define A276937 (MATCHING-POS 1 1 (lambda (n) (and (not (zero? (A276935 n))) (zero? (A276077 n))))))

CROSSREFS

Intersection of A276078 and A276936.

Topmost row of A276941 (leftmost column in A276942).

Cf. A276935, A276077.

Sequence in context: A016726 A047396 A276936 * A243373 A085304 A015843

Adjacent sequences:  A276934 A276935 A276936 * A276938 A276939 A276940

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 24 2016

STATUS

approved

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Last modified January 18 11:25 EST 2019. Contains 319271 sequences. (Running on oeis4.)