A353807 Numbers k such that A353802(k) / sigma(sigma(k)) is an integer > 1, where A353802(n) = Product_{p^e||n} sigma(sigma(p^e)).

1819, 5088, 7215, 7276, 9487, 9523, 11895, 13303, 14235, 16371, 20179, 21079, 21255, 24531, 24751, 24931, 25824, 29104, 30615, 32224, 33855, 36199, 37635, 37948, 38092, 38664, 40443, 40515, 41847, 43831, 44655, 45475, 45695, 45883, 46995, 48043, 48399, 53835, 54015, 54568, 55747, 56899, 56928, 59599, 60495, 61035

Offset: 1

Author

Antti Karttunen, May 08 2022

Keywords

• nonn

Comments

Numbers k such that A353805(k) = 1, but A353806(k) > 1.

Examples

			A353802(1819) = 10920 = 2*A051027(1819) = 2*5460, therefore 1819 is included as a term.
		

Links

• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A051027, A353802, A353805, A353806.

Cf. also A336561.

Programs

PARI

A051027(n) = sigma(sigma(n));
A353805(n) = { my(f = factor(n)); (A051027(n) / gcd(A051027(n), prod(k=1, #f~, A051027(f[k, 1]^f[k, 2])))); };
A353806(n) = { my(f = factor(n), u=prod(k=1, #f~, A051027(f[k, 1]^f[k, 2]))); (u / gcd(A051027(n), u)); };
isA353807(n) = ((1==A353805(n)) && (1!=A353806(n)));