A351538 Numbers k such that both k and sigma(k) are congruent to 2 modulo 4 and the 3-adic valuation of sigma(k) is exactly 1.

26, 74, 122, 146, 194, 218, 234, 314, 362, 386, 458, 482, 554, 626, 650, 666, 674, 698, 746, 794, 818, 842, 866, 914, 1082, 1098, 1154, 1202, 1226, 1314, 1322, 1346, 1418, 1466, 1514, 1538, 1658, 1706, 1746, 1754, 1850, 1874, 1962, 1994, 2018, 2042, 2066, 2106, 2138, 2186, 2234, 2258, 2306, 2402, 2426, 2474, 2498

Offset: 1

Author

Antti Karttunen, Feb 14 2022

Keywords

• nonn

Comments

All the terms of the form 4u+2 in A349745 (if they exist) are found in this sequence. As A351537 is the intersection of A191218 and A329963, and the latter has asymptotic density zero, so has this sequence also. It is conjectured that A351555(a(n)) is nonzero for all n, which would imply that the intersection with A349745 is empty. - Antti Karttunen, Feb 19 2022

Links

• Antti Karttunen, Table of n, a(n) for n = 1..25000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A191218, A329963, A349745, A351537.

Probably a subsequence of A351543. (See also A351550, A351555).

Programs

PARI

isA351538(n) = if(!(2==(n%4)),0, my(s=sigma(n)); (2 == (s%4)) && (1==valuation(s,3)));

Formula

a(n) = 2 * A351537(n).