A387160 Terms of the form prime * m^2 in A351554.

2, 3, 7, 20, 27, 28, 31, 127, 496, 567, 775, 2268, 3100, 8128, 8191, 27783, 131071, 403172, 524287, 3628548, 17389708, 32656932, 33550336, 127926848, 1087307452, 1248461136, 1408566348, 2147483647, 7802882100, 8589869056, 9785767068, 10362074688, 31211528400, 88071903612

Offset: 1

Author

Antti Karttunen, Aug 24 2025

Keywords

• nonn
• new

Comments

Conjecture: This sequence has no common terms with A228058. See comments in A386430.

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Intersection of A229125 and A351554.

Cf. A162642, A228058, A351555, A386430.

Subsequences: A000396\{6}, A000668.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351555(n) = { my(s=sigma(n),f=factor(s),u=A003961(n)); sum(k=1,#f~,if((f[k,1]%2) && 0!=(u%f[k,1]), (valuation(n,f[k,1])!=f[k,2]), 0)); };
isA387160(n) = (isprime(core(n)) && (0==A351555(n)));

Formula

{k | A162642(k) = 1 and A351555(k) = 0}.

Extensions

Terms a(29)-a(34) from Giovanni Resta, Aug 25 2025