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A238748 Numbers n such that each integer that appears in the prime signature of n appears an even number of times. 7
1, 6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 36, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 100, 106, 111, 115, 118, 119, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 177, 178, 183, 185, 187, 194 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Values of n for which all numbers in row A238747(n) are even. Also, numbers n such that A000005(n^m) is a perfect square for all nonnegative integers m; numbers n such that A181819(n) is a perfect square; numbers n such that A182860(n) is odd.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

EXAMPLE

The prime signature of 36 = 2^2 * 3^2 is {2,2}. One distinct integer (namely, 2) appears in the prime signature, and it appears an even number of times (2 times). Hence, 36 appears in the sequence.

The prime factorization of 1260 = 2^2 * 3^2 * 5^1 * 7^1. Exponent 2 occurs twice (an even number of times), as well as exponent 1, thus 1260 is included. It is also the first term k > 1 in this sequence for which A182850(k) = 4, not 3.

PROG

(Scheme)

(define A238748 (MATCHING-POS 1 1 (lambda (n) (square? (A181819 n)))))

(define (square? n) (not (zero? (A010052 n))))

;; Requires also MATCHING-POS macro from my IntSeq-library - Antti Karttunen, Feb 06 2016

CROSSREFS

Subsequences include A006881, A030229, A046386, A077448, A162142, A179690, A190108, A190465.

Subsequence of A000379, A007422 and A268390.

Cf. A000005, A181819, A182850, A182860, A238747.

Sequence in context: A276818 A325259 A320911 * A268390 A265693 A211484

Adjacent sequences:  A238745 A238746 A238747 * A238749 A238750 A238751

KEYWORD

nonn

AUTHOR

Matthew Vandermast, May 08 2014

EXTENSIONS

Second example added by Antti Karttunen, Feb 06 2016

STATUS

approved

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Last modified August 20 08:27 EDT 2019. Contains 326143 sequences. (Running on oeis4.)