login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A326148 Odd numbers > 1, not powers of primes, for which A326147(n) is equal to abs(A326146(n). 5
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 6 01:16 EDT 2020. Contains 334858 sequences. (Running on oeis4.)