A326148 Odd numbers > 1, not powers of primes, for which A326147(n) is equal to abs(A326146(n)).

15, 91, 207, 703, 847, 1023, 1891, 2701, 2725, 5551, 12403, 15043, 18721, 19359, 38503, 49141, 79003, 88831, 104653, 146611, 148951, 188191, 218791, 226801, 269011, 286903, 346957, 385003, 497503, 597871, 665281, 721801, 736291, 765703, 873181, 954271, 1056331, 1207359, 1314631, 1345873, 1373653, 1537381, 1755001

Offset: 1

Author

Antti Karttunen, Jun 10 2019

Keywords

• nonn

Comments

Odd numbers > 1, not powers of primes, for which A326146(n) [= (sigma(n)-A020639(n)-n)] is not zero and divides n-A020639(n).

Question: Are any of these terms present also in A326064 and A326074? None of the first 519 terms are. If such intersections are empty, then there are no odd perfect numbers.

Of the first 519 terms, 485 are semiprimes.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..519; all terms < 2^31
• Index entries for sequences where any odd perfect numbers must occur

Crossrefs

Cf. A020639, A046666, A326064, A326074, A326146, A326147.

Programs

PARI

A020639(n) = if(1==n, n, factor(n)[1, 1]);
A326146(n) = (sigma(n)-A020639(n)-n);
A326147(n) = gcd(n-A020639(n), sigma(n)-A020639(n)-n);
isA326148(n) = if((n>1)&&(n%2)&&!isprimepower(n), my(s=factor(n)[1, 1], t=n-s, u=sigma(n)-s-n); (u && !(t%u)), 0);