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

1,1

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

Prog

(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);

Crossrefs

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

Sequence in context: A320524 A218408 A048630 * A035163 A237516 A020242

Adjacent sequences: A326145 A326146 A326147 * A326149 A326150 A326151

Keyword

nonn

Author

Antti Karttunen, Jun 10 2019

Status

approved