A326181 Numbers n for which sigma(sigma(n)) = 3*sigma(n).

54, 56, 87, 95, 276, 308, 429, 446, 455, 501, 581, 611, 158928, 194928, 195072, 199950, 226352, 234608, 236432, 248325, 255678, 263504, 266192, 273050, 275415, 304575, 336903, 341162, 353675, 366575, 369425, 369843, 380463, 386313, 389463, 406565, 411725, 415925, 422303, 447587, 468743, 497333, 500993, 511829, 515267, 519557, 519677

Offset: 1

Author

Antti Karttunen, Jun 16 2019

Keywords

• nonn

Comments

Any odd perfect numbers must occur in this sequence, as such numbers must be in the intersection of A000396 and A326051, that is, satisfy both sigma(n) = 2n and sigma(2n) = 6n = 3*2n, thus in combination they must satisfy sigma(sigma(n)) = 3*sigma(n). Note that odd perfect numbers should occur also in A019283.

If, as conjectured, A005820 has 6 terms, then this sequence is finite and has 756 terms. - Giovanni Resta, Jun 17 2019

Links

• Giovanni Resta, Table of n, a(n) for n = 1..756 (first 169 terms from Antti Karttunen)
• Index entries for sequences where any odd perfect numbers must occur

Crossrefs

Cf. A000203, A000396, A005820, A019283, A051027, A087943, A272027 (3*sigma(n)), A326051.

Subsequence of A066961.

Programs

PARI

isA326181(n) = { my(s=sigma(n)); (sigma(s)==3*s); };