A344702 Positions k where A344695(k) is not multiplicative.

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

Offset: 1

Author

Antti Karttunen, May 27 2021

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

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

Subsequence of A013929 and of A024619.

Programs

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));