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A344702 Positions k where A344695(k) is not multiplicative. 4
108, 196, 200, 216, 288, 432, 441, 500, 540, 588, 600, 675, 676, 756, 784, 800, 864, 882, 980, 1000, 1080, 1125, 1188, 1225, 1323, 1350, 1372, 1400, 1404, 1440, 1444, 1500, 1512, 1521, 1568, 1728, 1764, 1800, 1836, 2000, 2016, 2028, 2052, 2156, 2160, 2200, 2205, 2250, 2352, 2376, 2400, 2450, 2484, 2548, 2592, 2600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers k with a factorization into coprime x and k/x with A344695(x) * A344695(k/x) <> A344695(k). - Peter Munn, 04 Jun 2021

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

For 108 = 4*27, A344695(108) = 8, although A344695(4) = 1 and A344695(27) = 4, and 1*4 != 8, therefore 108 is included in this sequence.

For 441 = 9*49, A344695(441) = 3, although A344695(9) = 1 and A344695(49) = 1, and 1*1 != 3, therefore 441 is included in this sequence.

PROG

(PARI)

A001615(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615

A344695(n) = gcd(sigma(n), A001615(n));

A344695mult(n) = { my(f = factor(n)); prod(k=1, #f~, A344695(f[k, 1]^f[k, 2])); };

isA344702(n) = (A344695(n)!=A344695mult(n));

CROSSREFS

Cf. A000203, A001615, A344695, A344696, A344697.

Subsequence of A013929 and of A024619.

Sequence in context: A323548 A338382 A338384 * A044340 A044721 A095050

Adjacent sequences:  A344699 A344700 A344701 * A344703 A344704 A344705

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 27 2021

STATUS

approved

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Last modified December 9 05:30 EST 2021. Contains 349627 sequences. (Running on oeis4.)